He said a meaningful return of flying this summer, needed to help airlines and travel companies survive after over a year of COVID-19 restrictions, would require the government to relax some measures.
But there is scant political appetite for doing so.
Ministers have said people should not go on holiday to countries which are not on the green list, and Prime Minister Boris Johnson said on Friday that it would not be extended any time soon because of the risk of new variants.
Heathrow said the limited reopening meant that it had 11,000 people flying out on Monday, up from 7,000 a day last week but well below the 120,000 typical at this time of year pre-pandemic.
BA said it was flying just a fraction of the 200 flights per day it would usually be operating in this period.
The United States, the Caribbean, France, Greece and Spain should all make it onto the green list before the summer, said the two bosses.
"We are calling on the government to help people to plan ahead by publishing a list of countries expected to be on the green list for the summer," said Heathrow's Chief Executive John Holland-Kaye.
The bosses also said fully vaccinated people should not require a COVID-19 test upon return from a low-risk country, and that a cheaper lateral flow test should be sufficient for those who are not vaccinated.
Multiple COVID-19 testing requirements can cost more than the flight for some people. Different country requirements are also hampering a travel bounceback.
At Heathrow, there was joy for some, permitted to travel again after four and a half months of lockdown restrictions.
Erica Stolton, 29, was heading to Madrid to introduce her baby to her family for the first time. "It feels absolutely magical. It's been really hard, the situation with this pandemic," she said.
Some others were left disappointed. Jane Sunley, 60, was turned away from her flight to Mykonos, Greece on Monday for not having filled in forms 24 hours before departure.
"We'll lose our flights, we'll lose our hotel, there's not another flight until Friday," she said. "It's not simple, is it"
Prime Minister Boris Johnson said on Friday a tough border regime would stay in place for the foreseeable future. The UK has low overall infection rates thanks largely to the success of its vaccine rollout, but concerns are growing about a fast-spreading variant first identified in India.
(Reporting by Sarah Young; Writing by Kate Holton; Editing by Paul Sandle, Michael Holden and Jan Harvey) ((email@example.com; 0044 207 542 8560; Reuters Messaging: firstname.lastname@example.org))