Passengers arriving at Heathrow face waiting up to two and a half hours to get through passport control.
Border Force at the UK’s largest airport failed to meet waiting time targets more than 100 times on one day last month.
Its agreed service standards are to clear European Economic Area passengers within 25 minutes and non-EEA arrivals within 45 minutes 95% of the time.
But on December 29 targets were missed on 101 occasions when queue times were checked every 15 minutes during the day.
In 17 cases, queue times for non-EEA passengers exceeded 85 minutes and twice surpassed that time for EEA passengers.
The longest queue time was 150 minutes at Terminal 4 for non-EEA travellers, according to a leaked report seen by the Mail on Sunday.
Lucy Moreton, general secretary of the Immigration Service Union, said: “It’s not uncommon to fail to meet queuing-time targets at Heathrow because of the huge staffing pressures.”
A Heathrow spokesman said: “We have been working with Border Force on improving waiting times.”