The boss of EasyJet has said testing requirements under a proposed "traffic light" system for international travel would be too expensive.
Under the system, no isolation would be necessary on return to the UK from so-called "green" countries.
But pre-departure and post-arrival tests would be required, potentially costing up to £200 each.
Johan Lundgren said: "You wouldn't open up international travel for everyone, but only those who can afford it."
Mr Lundgren told the BBC's Today programme that the cost of getting the tests would exceed a typical EasyJet fare.
On Sunday, plans for a risk-based system to restart foreign travel were outlined, in which countries would be classified as "green", "amber" or "red" based on their infection rates and vaccination coverage.
However, while the prime minister said he was "hopeful" that non-essential foreign travel could begin again on 17 May, he added that more data was needed before a firm decision could be taken.
Mr Lundgren said: "If you are ticking all of those boxes to become a green destination… [Multiple tests] don't make sense to me and it would add to cost and complexities."
He said that the testing requirement for those countries was "concerning", but added that he still expected holidays in the summer months of July and August would be able to go ahead.
Scientists and ministers recently warned that holidays to destinations such as France, where Covid cases are rising, are "unlikely". But Mr Lundgren said: "There's a huge amount of pressure building up now in these countries to get going and make sure they can follow the example of the UK in its vaccine rollout."
Other travel industry figures also called for clarity following the Prime Minister's latest announcement on lockdown restrictions easing.
The Business Travel Association said the announcement was "beyond disappointing" and called for "a clear pathway to international travel and trade".
Its chief executive, Clive Wratten, said moves to open borders had "once again been kicked down the road".
"The business travel industry continues to be crippled by today's lack of movement," he added.
The boss of travel firm Thomas Cook, Alan French, also told the BBC's Wake Up to Money that a lack of clarity around what type of tests might be required for passengers and when they would need to be taken was a let-down.
He said that overall, there were "glimmers of good news", in that the earliest date for travel resuming on 17 May was not pushed back. "But actually, the details were missing and that was disappointing," he said.
'Disappointed'
On Monday, Mr Johnson said he did not want to see coronavirus re-imported from abroad and urged people to wait for a report from the Global Travel Taskforce on 12 April.
But Gemma Antrobus, owner of independent travel company Haslemere Travel, warned that business owners like herself faced a difficult path.
"Disappointed is putting it mildly. Where we hoped confidence would start to pick up, and more people would be interested in booking holidays… that just won't come this week."
She added that some customers had now moved bookings for holidays five times amid changing restrictions.
"Every week we don't have that confidence from consumers, business owners like myself just wonder what lies ahead."
Source: BBC
