Holidaymakers could be sat waiting on planes as queues at airports could exceed four hours when foreign travel fully resumes next week.
Passengers could be forced to remain in planes on the runway to prevent lengthy waiting time in airport terminals.
Britain's border infrastructure cannot yet cope with the number of travellers expected when the government lifts quarantine requirements for amber countries, unions have warned.
Travel agents and airlines have reported a fivefold increase in holiday booking after the government announced it was dropping quarantine rules for fully vaccinated travellers returning from amber list countries.
Watch: COVID-19 - Bookings for flights to amber list countries up by 400% after no-quarantine announcement
From July 19 passengers who have had both jabs will not have to quarantine for 14 days when they return from amber list countries which include France, Spain, Portugal and Italy.
The waiting in aircraft contingency plan is said to be one of the options being considered by Heathrow and other large airports if border control queues exceed four hours.
Lucy Moreton, from the ISU immigration union which represents frontline border staff, told the Times: "This decision will open up foreign travel to a large number of new travellers. But we are not set up to cope with that sort of demand. There is no way that the border can maintain that level of checks as the number of travellers increase.
"We've got away with it so far because the number of travellers are so low. But even at this point we're seeing queues of one to two hours. From the number of bookings we've seen already, we'll easily see three, four-hour queues."
Holidaymakers will still have to fill out a passenger locator form with details of their home address and confirmation that a PCR Covid test has been booked on their return.
Border Force agents will also have to check all passengers' documents as they pass through passport control.
Transport secretary Grant Shapps has already warned travellers to expect long queues when checking in for their return flights as extra time will be needed to check documentation.
It comes as many people arriving at Heathrow on Monday morning faced more than two hour waits in Terminal 5 departures.
More than 100 staff members had reportedly been ordered to self isolate by the NHS Test and Trace app, causing the delays.
A Heathrow spokesman said: “We have activated additional team members to assist passengers with their journeys and the operation has now returned to normal. We apologise to our passengers for any inconvenience caused.”
A government spokesman said systems were being upgraded and additional Border Force officers deployed to speed up the queues.
He added: “Our utmost priority is protecting the health of the public and our enhanced borders regime is helping reduce the risk of new variants being transmitted.”
Watch: Why anti-nausea bands are a travel essential