Airport operator BAA has complained that immigration queues at Heathrow are "unacceptably" long, just weeks before the Olympic Games are due to begin.
Last week some passengers faced waits of up to two-and-a-half hours - raising fears that the immigration system may not be able to cope with the arrival of thousands of athletes.
BAA said the Home Office had promised all Border Force desks at Heathrow would be manned during the peak Olympics arrival times.
But it added that the Home Office should be "delivering a good experience for regular passengers as well as Olympic visitors".
According to the Daily Telegraph there were half-mile queues at Heathrow's Terminal 4 last Friday, while pictures in the paper showed empty immigration desks.
The Immigration Service Union, which represents 4,500 border staff, told the paper that the present problems were being made worse as only about half the current workers were fully trained to allow passengers from anywhere in the world entry.
A Border Force spokeswoman said the queues at Heathrow had been "less than an hour" and that extra staff had been deployed to deal with them.
She went on: "We are fully prepared for the busy Olympic period and will be implementing our well-rehearsed plans.
"This includes staffing all immigration desks at key ports whenever necessary during the peak Olympic and Paralympic arrivals period."
New figures show that the Border Force failed to meet its targets for getting non-EU passport holders through immigration at Heathrow last month.
The agency aims to get 95 percent of passengers through within 45 minutes, but at Terminal 5 they only managed 76 percent.
The figures were released on BAA's website after the Government admitted the Border Force needs to change the way it operates. Large queues built up at passport control at the airport last week, with some passengers waiting for up to three hours.
However, the Border Force did meet its targets for EU passport holders, meaning that 95 percent of passengers were processed in less than 25 minutes.
Terminal-by-terminal figures at Heathrow in April 2012 - percentage of non-EU passport holders processed within 45 minutes:
Government plans to bring in 80 extra staff to tackle unacceptable delays at Heathrow Airport are like "putting a sticking plaster on a serious injury", a union warned today.
Damian Green admitted the Border Force needs to change the way it operates & said extra staff would start work this month.
But Mark Serwotka, general secretary of the Public and Commercial Services (PCS) union, warned: "Drafting in staff from other areas of an already overstretched agency is like putting a sticking plaster on a serious injury, it will do nothing to stop the inevitable from happening."
Labour said some 1,500 Border Force staff were being cut as the management of Britain's borders drifted "from one shambles to another".
It came as a senior Games boss warned that the delays were damaging the Olympic mission to promote Britain abroad and win business.