When the defence secretary, Philip Hammond, released a statement on 15 December confirming that thousands of British troops would help bolster secu..., the next day's headlines took care of themselves. "Snipers, jets and 13,500 troops on Olympics duty," declared the Mail.

In the months beforehand, as the army and police had bickered about who should step in, Olympic organisers had turned to the giant security firm G4S. The company, which was already enlisted to provide 2,000 guards, then upped its contribution, supplying more than 10,000 and managing the training for 23,700 personnel – including the military. For this, it billed the organisers at Locog an extra £200m, the contract more than tripled from £86m to £284m.

In terms of G4S's global financial might, the deal was relatively insignificant, but it revealed its capacity and ambition: as the public sector squabbled, it saw a business opportunity.

G4S began life in the UK one evening in 1935 when four men cycled off on the first security round for the newly formed London firm Night Watch Services. Since then, through a series of acquisitions and mergers – most notably in 2004 when Securicor merged with the Danish company Group 4 Falck – it has become a global giant of dizzying proportions. The company now has 657,000 staff operating in more than 125 countries, making it one of the world's largest private-sector employers.

Its turnover has almost doubled since 2005, standing at £7.5bn in 2011, despite the global economic turmoil. Its interests range across five continents – from running security at airports to protecting VIPs in Iraq and India and Iraq; from guarding key corporate interests in Africa to supplying security systems to the Pentagon; and from protecting ships from pirates in the Indian Ocean to providing security at Wimbledon.

In the UK, which remains its core market, the company is increasingly moving into areas previously run by the government: prisons; policing; building and managing the GCHQ communications base; being a key operator of the government's controversial welfare to work programme; running immigration detention centres; and providing caretakers, cleaners and security at schools and hospitals.

For many critics the company is, in effect, operating a shadow state. According to Mike Allen of the City analysts Panmure, although government contracts made up just 15% of G4S's total revenue in 2006, that had jumped to 27% last year and the company says it is now a growing sector worth 50% of its UK business.

"The scale of G4S and its rapid growth is quite astonishing," said Professor Stephen Graham from Newcastle University and author of Cities Under Siege, who has been studying the company. "It is quite possible to conceive a near future where, from cradle to the grave, it is G4S that is there at almost every stage, taking the place of what used to be public services."

As G4S declares on its website: "In more ways than you might realise, G4S is securing your world."

One of the most important areas of growth for G4S has been in the UK's criminal justice system as successive governments "rolled back the state" for private companies to take on previously public services. It opened its first prison in 1997, and now runs six institutions across England. The latest – HMP Oakwood – opened in Wolverhampton in April.

Now G4S has its sights on the UK's police service. Last month, when the 17 members of the West Midlands police authority gathered in the main committee room at police headquarters in Birmingham to discuss the biggest police privatisation deal to date, G4S's bid was near the top of the pile. If the proposals go through, the successful firm could be handed contracts to investigate crimes, carry out forensics and run private "prisoner removal units", as part of a £1.5bn deal that includes Surrey police.

At a Unite union meeting in London in May, police staff from the West Midlands, including drivers, telephone controllers and forensics officers, argued the proposals would change the way policing was done in the UK. Unite's national officer, Peter Allenson, said: "Our members are totally in the dark about what this will mean for the service in practice. This is not the back office – we are talking about the privatisation of core parts of the police service including crime investigation, forensics, 999 call-handling, custody and detention and a wide range of police services."

Staff say that the radical plans are being pushed through without proper public scrutiny, citing a recent poll for the union in which 77% of those asked in the West Midlands were unaware of the proposed changes. In the face of rising public concern, both Surrey and the West Midlands forces have announced that they are to slow the timetable to allow more public consultation.

But the Guardian has learned there are already signs that more forces are preparing to follow a similar route. Ten more forces, including Cambridgeshire, Bedfordshire and Hertfordshire, have announced they are considering privatising some services in an attempt to tackle a funding shortfall created by government cuts.

In his office in the new regional HQ in Victoria, central London – a stone's throw from government decision-makers in Westminster and Whitehall – David Taylor-Smith, head of G4S for the UK and Africa, says greater private-sector involvement in policing is long overdue.

"We would never try to take away core policing functions from the police but for a number of years it has been absolutely clear as day to us – and to others – that the configuration of the police in the UK is just simply not as effective and as efficient as it could be. Consecutive home secretaries have tried to wrestle with that issue and usually not got very far … I think there is an unusual set of circumstances at the moment, that is budgetary pressure and political will."

The company already has a significant toehold in UK policing. In April it began work on a £200m contract in Lincolnshire where it will design, build and run a police station in a deal that has seen more than 575 public-sector police staff transfer to the company. Alarm at the move was heightened when it emerged that 200 staff had been issued with uniforms that bear the G4S logo alon...

The company also runs more than 500 police cells in Lancashire, south Wales and Staffordshire and Taylor-Smith believes these contracts are just the start. He expects police forces across the country to sign up to similar deals to those being hammered out in the West Midlands and Surrey over the next five years. "For most members of the public, what they will see is the same or better policing and they really don't care who is running the fleet, the payroll or the firearms licensing – they don't really care."

High-profile billion-pound contracts are not the only area of policing that G4S is engaged in. The company has 17,000 former police officers on the books as part of its Policing Solutions database. The site works like a private police employment agency, offering former officers, usually on short-term contracts, to forces around the UK and often the world.

In the trade, these former detectives are known as the "30-yearers" – police officers who have retired after 30 years' service and then take up contracts in the private sector. A quick flick through the Policing Solutions website reveals the company is looking for a "major crime investigator" offering £25,000 a year: "Ideal for former detectives with excellent report-writing skills who have recent murder investigation experience." Or an investigator whose salary is described as "competitive" and who should be "from either a UK policing or military background". You will need "extensive experience of working on numerous major investigations".

"For many of them, not only is it a way of them reusing their skills," said Taylor-Smith. "They can put the gang back together that they used to work with."

G4S says that its staff have been involved in many major investigations over the past few years – it supplied five former detectives to help with the investigation into the murder of Jo Yeates in December 2010. Indeed the company says most of the 43 police forces in England and Wales have called on its services at some point.

Despite its extensive involvement Taylor-Smith is adamant the company has no intention of taking over core policing duties, adding: "You can see when you are getting close to the boundary [for private-sector involvement] by public, media and political debate.

"There are definitely areas that must remain core functions of the state, so if you are looking at the armed forces, the armed forces maintain the right to use lethal force. If you are looking at policing core policing functions, the power of arrest and the ability to detain people, it is absolutely right that it should remain in the public sector."

But the scale of G4S's private police database and its increasingly important role in police outsourcing has led some to fear it is slowly undermining publicly backed and paid-for forces. Allenson from Unite said: "This is not about making the police force more efficient – it is about transferring our crucial public services to the private sector, which has a totally different ethos and set of priorities. Privatisation has nothing to do with making our streets safer. It has everything to do with profit."

Mel Kelly, a journalist who has written about G4S for the Open Democracy website, says it is already possible to construct a scenario where a crime is committed and at each stage it is G4S rather than the police who are involved. "It is quite conceivable now to have a violent crime where a scene of crime officer employed by G4S is dispatched, a forensic team employed by the company collects swabs dispatched to G4S forensics, a suspect is held in cells run by G4S and appears before a magistrate trained by the company. He is convicted and sent to a G4S prison. On probation he attends a G4S work programme wearing a G4S electronic tag. This is not a dystopian future but the reality as it is now."

Others say the scale of private-sector involvement in UK policing raises wider concerns, such as what the long-term impact will be of hollowing out public services. Is there a limit to what the private sector can provide? What control does the public have if things go wrong?

Professor Graham said: "With virtually no public debate or democratic scrutiny, crucial pieces of our criminal justice and public security systems are being taken over by private security corporations. The long-term implications for public justice, accountability, transparency and equality are likely to be very grave indeed."

Since it first began to operate in the UK's criminal justice sector, G4S has convinced some of those who were initially hostile that it can be a force for good – improving levels of service and efficiency. Over the years a string of senior politicians and public figures have taken up positions at the firm, including the former home secretary John Reid and ex-Met commissioner Paul Condon.

A former director general of the prison service, Martin Narey, who now has a contract with the firm as a consultant on decency in G4S prisons, says he was once vehemently opposed to private-sector involvement in the prison service before he was appointed in 1998.

"When I was working as a governor in prisons in the north-east I felt very strongly about the private sector … indeed I met ministers and told them how reprehensible it was that we should be having private prisons. But as director general I opened 10 of the first 11 private prisons and I was delighted to do so."

Narey said his main concern had always been that prisons should treat inmates with a level of decency often missing in state-run institutions.

"The private sector just did things. The places were gleaming and they had emphasis on getting people out of cells, and I had to quickly revise my opinion."

G4S opened its first prison at Altcourse in Liverpool in 1997. "Altcourse changed me greatly. Shortly after I became director general I had been to Liverpool prison. It was awful as ever, pretty grimy, staff not remotely positive about some the things I was talking to them about – certainly about decency and rehabilitation. And prisoners were overwhelmingly locked up and there was a sense of disrespect about the place.

"Altcourse was very different. Here I sat in reception and heard a young prisoner come forward and be called – say his name was John Brown – he was called Mr Brown, something I had never heard in my life as a prison officer."

During his time in charge of prisons Narey said he worked closely with G4S and Taylor-Smith. "I found [him] absolutely committed to running decent prisons, absolutely in tune with what I wanted … the fact they made a profit didn't matter to me because ultimately they ran good prisons."

Narey said the success of private prisons was due partly to the absence of the prison officers' association, which he said was an organisation that was often "resistant to change".

"It was also that ... they recruited the best people and partly just an acceptance that I was the customer and when I said I wanted the prisoners to be treated with dignity they treated people with dignity. The best thing of all about the private sector was that we could then use that as a tool to improve public sector prisons. For the first time public sector prisons fearful that there was someone else that could do the job began to improve massively."

Professor Alison Liebling is widely acknowledged as the leading expert in the field and, with colleagues at Cambridge University, she conducted a comprehensive study into the relative performance of private versus public prisons. She said the picture was not as clear cut as "private is best", partly because staff in them were relatively inexperienced, fewer in number and less professionally powerful, which could lead to a "slightly naive and permissive model of order". This could mean that prisoners "may have better and more constructive experiences in the best 'traditional-professional' public-sector prisons".

G4S was not always such a dominant force in Britain. In the early 1990s Group 4, as one arm of the company was then, was viewed as something of a national joke after several prisoners escaped while being transported by the company. Since then it has been involved in a number of controversies – including the death in October 2010 of Jimmy Mubenga. The 46-year-old Angolan deportee died while being forcibly restrained on a flight from Heathrow. Three G4S guards were arrested on suspicion of manslaughter. They remain on bail.

The company had been dogged by allegations of abuse against detainees and poor levels of training among its staff while running the contract. Four whistleblowers who submitted evidence to the home affairs select co... in the aftermath of Mubenga's death said the company had been warned repeatedly by its own staff that potentially lethal force was being used.

G4S said that although it had requested the details of the allegations it had not received any specific information. "We would obviously be keen to investigate these allegations but have not been able to conduct a review or take any action without seeing the evidence," said a spokesman.

G4S lost the UK removals contract to Reliance, who took over in May last year. However, it recently won a £203m deal with the UK Border Agency to house asylum seekers across Britain – a service that was previously provided by regional public sector consortiums and housing associations. The deal has raised familiar concerns among asylum rights campaigners who say a security company should not be acting as a landlord to asylum seekers who are often vulnerable and the victims of torture.

John Grayson from the South Yorkshire Migration and Asylum Action Group, cites Mubenga's death in G4S's care, and the 773 complaints lodged against G4S in 2010 by detainees including 48 claims of assault, three of which were upheld, as evidence that the company should not be working with asylum seekers. G4S said the number of substantiated complaints against its employees – 25 cases – was "extremely low" but it took each seriously.

Charlie Edwards of the international thinktank Rand says G4S's global reach means it has been more successful than almost any other company in cashing in on government contracts. "G4S are a global player and when companies have outsourced parts of their business to other countries they have their own security arrangements in place and if the country cannot meet them then companies like G4S come in and manage them. The era of globalisation has been a real boom period for private security companies. When the state is ineffective the private sector is seen as the dream companion."

But in the rain outside the company's AGM in central London earlier this month, protesters who had gathered to vent their anger at G4S's global activities and particularly its involvement in Israeli prisons did not share this vision of a "dream companion". Dozens of activists from the Palestine Solidarity Campaign, Global Women's Strike and the All African Women's Group handed shareholders an "alternative annual report" that criticised the conduct of the security company and held banners which read "G4S global threat to freedom".

A few weeks earlier, in his office on the other side of London, Taylor-Smith insists such concerns are deeply misguided. G4S's work in prisons, police and the criminal justice system, he says, does not mean that some "public-sector ethos" has been lost.

"I have always found the notion patronising and insulting that the public sector has an exclusive franchise on some ethos, spirit, morality. It is nonsense. The thought that everyone in the private sector is primarily motivated by profit and that is why they come to work is just simply not accurate … We employ 675,000 people and they are primarily motivated by pretty much the same as would motivate someone in the public sector."

But as the company prepares for its latest high-profile role, this time helping secure the London Olympics, many believe there needs to be a public discussion about the long-term impact of G4S's runaway growth and a broader conversation about the limits to private-sector involvement in public services.

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EXPOSING THE ISRAELI OCCUPATION INDUSTRY

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G4S Israel (Hashmira) (ג'י פור אס ישראל (השמירה