Private companies will be running large parts of the UK's police service within five years, according to the world's biggest security firm.

David Taylor-Smith, the head of G4S for the UK and Africa, said he expected police forces across the country to sign up to similar deals to those on the table in the West Midlands and Surrey, which could result in private companies taking responsibility for duties ranging from investigating crimes to transporting suspects and managing intelligence.

The prediction comes as it emerged that 10 more police forces were considering outsourcing deals that would see services, such as running police cells and operating IT, run by private firms.

Taylor-Smith, whose company is in the running for the £1.5bn contract with West Midlands and Surrey police, said he expected forces across the country to have taken similar steps within 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," he said.

G4S, which is providing security for the Olympics, has 657,000 staff operating in more than 125 countries and is one of the world's biggest private employers. It already runs six prisons in the UK and in April started work on a £200m police contract in Lincolnshire, where it will design, build and run a police station. Under the terms of the deal, 575 public sector police staff transferred to the company.

Taylor-Smith said core policing would remain a public-sector preserve but added: "We have been long-term optimistic about the police and short-to-medium-term pessimistic about the police for many years. Our view was, look, 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."

Concern has grown about the involvement of private firms in policing. In May more than 20,000 officers took to the streets to outline their .... The Police Federation has warned that the service is being undermined by creeping privatisation.

Unite, the union that represents many police staff, said the potential scale of private-sector involvement in policing was "a frightening prospect". Peter Allenson, national officer, said: "This is not the back office – we are talking about the privatisation of core parts of the police service right across the country, including crime investigation, forensics, 999 call-handling, custody and detention and a wide range of police services."

Taylor-Smith said "budgetary pressure and political will" were driving the private-sector involvement in policing but insisted that the "public sector ethos" had not been lost.

"I have always found it somewhere between patronising and insulting the notion that the public sector has an exclusive franchise on some ethos, spirit, morality – it is just nonsense," he said. "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."

In the £1.5bn deal being discussed by West Midlands and Surrey police, the list of policing activities up for grabs includes investigating crimes, detaining suspects, developing cases, responding to and investigating incidents, supporting victims and witnesses, managing high-risk individuals, managing intelligence, managing engagement with the public, as well as more traditional back-office functions such as managing forensics, providing legal services, managing the vehicle fleet, finance and human resources.

Chris Sims, West Midlands chief constable, has said his force is a good testing ground for fundamental change as he battled to find £126m of savings. He said the armed forces had embraced a greater role for the private sector more fully than the police without sparking uproar.

But a home affairs select committee reports said many of the policing contracts being put up for tender amounted to a "fishing expedition". MPs added that they were not convinced the forces understood what they were doing. The committee chair, Keith Vaz, said: "The Home Office must ensure it knows what services local forces wish to contract out before agreeing to allow expenditure of £5m on what is little more than a fishing expedition."

Cambridgeshire, Bedfordshire and Hertfordshire police announced this month that they were considering privatising some services in an attempt to tackle a £73m funding shortfall created by government cuts. Police authority members in the three counties will be asked to consider how services including HR, finance and IT could be outsourced in line with the G4S contract in Lincolnshire as part of a joint recommendation made by the three chief constables.

It has also emerged that Thames Valley, West Mercia, Warwickshire, Staffordshire, Gloucestershire, Wiltshire and Hampshire forces have begun a tendering process to outsource the running of 30 custody suites and 600 cells.

A Home Office spokesperson said, "Policing is not being privatised — core police functions will continue to be delivered by sworn officers and no police powers will be given to private contractors beyond the limited powers allowed by the last government.

But he said there was potential for a bigger role for private companies in future. "The private sector can help to support delivery of police services better and at lower cost, for example providing staff for control rooms and custody centres, releasing officers for frontline duties."

• This article was amended on 21 June to add a quote from a Home Office spokesperson.