Heathrow Airport chief executive John Holland-Kaye rejected calls for overseas trips to be restricted for the rest of the year, saying there was "no reason" why the UK could not allow quarantine-free travel with more countries.
Britain's green list of travel destinations allows for relatively unrestricted travel between 12 countries and territories.
Forty-three countries are on the red list, requiring British residents to quarantine in an approved hotel for 10 days at a cost of £1,750 ($2,467).
Every other country was placed on the amber list - meaning travellers must quarantine at home for 10 days and take PCR tests on days two and eight.
The new system was put in place after the ban on leisure travel was lifted on Monday.
However, University of Oxford professor and government vaccine adviser Sir John Bell said foreign holidays were "not a good idea" this year because of the risk posed by Covid outbreaks.
"We aren't at the peak of this thing globally at all yet, we're still going up the mountain," he told Times Radio.
“So having people flying around and coming back with whatever local variant they run into, that is not a good idea in my view. People just have to get used to the fact that Cornwall or Bournemouth or wherever is not so bad - and they should just enjoy the summer and then we can get back to this properly when things settle down.”
Health Secretary Matt Hancock also appeared to voice reservations about foreign travel, saying holidays in amber list countries should not happen.
“People should not travel to amber or red list countries unless it’s absolutely necessary, and certainly not for holiday purposes,” he said.
Asked about the comments, Mr Holland-Kaye said the green list was very small and should be expanded “quite significantly over the next month or so”.
"There are countries such as the US and Caribbean which have very similar characteristics to Portugal. There is no reason why those shouldn't open up later this month. Similarly, Greece and Spain should be coming on to the green list," he told Sky News.
“What we’d like to see from the government is a list of countries they think, based on current trajectory, should be on the green list this summer, so British people can book with confidence, so they can plan ahead for July and August, and the airlines and travel industry can gear up as well.”
British Airways chief executive Sean Doyle spoke of the toll of separating relatives for extended periods.
“There’s a human cost to this, in that a lot of people have been separated from friends and family for over 12 months now,” he told the BBC.
"That's a segment that we see grow, and a lot of people who are here today are taking the opportunity to reunite after a long period of separation."
Paul Charles, director of The PC Agency travel consultancy, said: “People want their livelihoods back”.
He suggested the government was advising against travel because of concerns that there are not enough border officers to process a surge in arrivals.
“It is up to travellers if they want to self-isolate on their return from an amber country,” he said on Twitter.
Prime Minister Boris Johnson said people should take part in new freedoms with a “heavy dose of caution” to prevent further outbreaks.