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Leaked figures obtained by the Labour Party reveal that around 880 officers (10%) have been cut from the UK Border Force since 2010.

A further 1,550 officer posts could go by 2014/15, the ´óÏó´«Ã½ understands.

Shadow home office minister Yvette Cooper said ministers were being complacent over the level of chaos at Heathrow airport border control.

Immigration Minister Damian Green said 80 extra staff were being drafted in to cut queues, among other measures.

Prime Minister David Cameron, who met Home Secretary Theresa May for an update on Tuesday morning, told ministers they must admit there is a problem at the BAA-owned airport.

He said, "we've got to grip this," ´óÏó´«Ã½ political editor Nick Robinson was told.

The Public and Commercial Services union warned the government was "putting a sticking plaster on a serious injury" by drafting in staff from other areas to work at Heathrow.

Mark Serwotka, its general secretary, said: "It will do nothing to stop the inevitable from happening. Everyone can see that the Government's obsession with austerity isn't working and that what UK Border Agency needs is more staff, not more cuts."

Mr Green visited Terminal 3 at the London airport on Tuesday during a quiet period, when queues were around five minutes long and around half the border control desks were manned.

He said the issue was not just about staff numbers, but about how and when they were deployed, adding the Border Force needed to be more flexible.

"Of course there is a problem - that is why I have spent some time explaining what we are doing about it," he admitted.

He said airports were taking "significant steps" to ensure the right channels were open at the right time.

A new central control room is being established at Heathrow to mobilise teams of border staff at terminals where queues may be beginning to build up.

A new rota system would begin in May which will make the system more flexible, and he guaranteed that all border control desks would be fully manned during the London Olympic Games, which start on 27 July.

´óÏó´«Ã½ home affairs correspondent Tom Symonds said the central cause of the issue was that staff numbers were cut on the basis that more selective passport checks would be done, then the government decided to reintroduce the full checks.

Ms Cooper is calling for the Home Office to publish their full figures on waiting times at every terminal at Heathrow and other airports.

"The home secretary needs to take charge of this chaos and get it sorted out. Leaving families to struggle with tired kids in long queues, or delaying business travellers because of poor management or the scale of cuts, is unacceptable," she said.

Sir Keith Mills, deputy chairman of Olympic Games organiser Locog warned the issue was damaging the Olympic mission to promote Britain abroad and win business.

He told the London Evening Standard: "The damage is being done right now."

Heathrow's owner BAA, which earlier urged the Home Office to address the issue, said it welcomed the government's recognition that the queue times were "unacceptable".

"We are encouraged by the announcement of additional border resources for Heathrow and welcome the new sense of urgency being shown by the government to tackle this problem," a spokewoman said.

Earlier, airline boss Willie Walsh accused the government of misleading the public over the length of the wait.

Mr Green claimed on Monday that non-EU nationals were waiting no longer than 90 minutes to enter the country.

But Mr Walsh - the boss of British Airways' parent company IAG said a more-detailed analysis using data and CCTV footage from Heathrow's owners BAA showed some passengers queued for two hours and 31 minutes on 27 April.

Between January and March, the average waiting time across all UK airports was six minutes for UK and EU citizens, and 25 minutes for non-EU passengers.

A Border Force spokesperson said: "As passenger numbers increase in the run up to the Olympics we are fully prepared to manage busy periods and will be implementing our plans.

"The Border Force will ensure that all immigration desks at Heathrow and other key ports and airports in the south east are fully staffed during peak periods over the summer."