Heathrow has said that long queues caused by extensive Covid checks at the airport are becoming "untenable".
Chris Garton, chief solutions officer at Heathrow, told MPs on the transport committee that some travellers faced waits of up to six hours.
On more than one occasion police had had to intervene because queuing was "not something passengers want to do", he added.
Foreign travel is only permitted for certain reasons at the moment.
Mr Garton said that all passengers, regardless of nationality, had to be thoroughly vetted before they left or entered the UK to ensure they complied with coronavirus legislation.
However, he said that the queues would become a "much bigger" problem if rules on foreign travel are relaxed on 17 May, as the government is planning.
Currently, he said about 10-15,000 people arrive at the airport each day, and "certainly more than half are having delays in excess of 2-3 hours each day".
He said the current system is a "tremendous burden on officers at the border" and that the Home Office had not provided enough officers.
"We would like to see more resources at the border," he told the MPs.
He said maintaining social distancing was hard as the airport was never built to "have so many people held up" in queues.
The BBC has contacted the Home Office for comment.
People in England can start thinking about booking foreign holidays again this summer, Transport Secretary Grant Shapps said last week.
But he said the cost of the Covid tests required needed to be driven down, amid criticism from the travel industry.
Mr Shapps has gave more detail on the traffic light system which will see countries graded on their risk.
Passengers will have to take the tests before leaving and on returning - even from low-risk "green" countries.
