The minister claimed that the union leader did not have the support of most border guards, adding: "He must be losing confidence that what he is doing actually represents the views of his members.

"This is the wrong time to pursue a grievance. Even our most militant unions can recognise that this is not the moment."

The strike is planned for what Mr Hunt predicted would be the busiest ever day at Heathrow Airport but, he said, he was confident enough border officials would turn up to work.

To staff all the desks at Heathrow, a minimum of 550 guards need to be on duty, and the minister said: "We have 584 shifts now confirmed for Thursday despite the strike, so I am very confident we will get through.

"We have can be very confident in the contingency plans. Queues at Heathrow have been the dogs that didn't bark."

Politicians and Olympics staff are increasingly irritated at the actions of some trade union leaders, as hundreds of thousands of athletes, sporting officials and spectators pour into London for the Games.

The capital's over-burdened transport system is at risk of even further strain, after some London Underground staff, who have already been promised an Olympics bonus of £1,000, threatened to begin a work-to-rule regime.

Members of the Rail, Maritime and Transport union are protesting about the use of casual workers on the Tube, and the way that the Olympics pay deal is due to be implemented.

A proposed strike during the Games by London bus drivers was averted only when they secured a bonus of more than £500.