Airport operator BAA today said recent immigration queues at Heathrow were “unacceptably” long.
Last week some passengers faced waits of two-and-a-half hours to get through immigration at the west London airport.
With thousands of athletes due to arrive at Heathrow over the next three weeks, there are concerns the immigration system - the responsibility of the Home Office - may not be able to cope.
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”.
Under its targets, the Border Force must get non-EU passport holders through immigration at Heathrow in less than 45 minutes for 95% of the time.
The target for EU passport holders at Heathrow is less than 25 minutes for 95% of the time.
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.
A BAA spokesman said today: “Immigration is a matter for the Home Office. The Home Office has said that from July 15 all Border Force desks at Heathrow will be open during peak arrival periods.
“Immigration waiting times for passengers during peak periods at Heathrow in the last few days have been unacceptably long and the Home Office should be delivering a good experience for regular passengers as well as Olympic visitors.”
The Immigration Service Union, which represents 4,500 border staff, told the Daily Telegraph 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 queue breaches 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."
House of Commons Home Affairs Committee chairman Keith Vaz said: "I am extremely concerned that, despite repeated promises from the Home Secretary and the Immigration Minister, passengers arriving at Heathrow continue to wait an inexcusable amount of time to clear immigration.
"I have written to Damian Green today, ahead of his appearance before the committee next week, asking him to provide accurate data on waiting times and to explain how these queues have been allowed to build up again.
"With only four weeks to go until the Olympics, ministers must ensure the Border Force have all the resources they need to provide swift and thorough checks at our borders."