They issued the plea at a joint virtual press conference held ahead of the meeting between Mr Johnson and Mr Biden in advance of the G7 summit in Cornwall.
The US is currently on the UK’s amber list, which means arriving travellers must self-isolate for 10 days.
Virgin Atlantic chief executive Shai Weiss said travellers should be able to enter the UK from the US without needing to quarantine.
He said: ‘There is no reason for the US to be absent from the UK green list. This overly cautious approach fails to reap the benefits of the successful vaccination programmes in both the UK and the US.
UK passengers arrive at Heathrow Terminal 2 from Portugal after dashing home to avoid having to quarantine at home
Passengers arrive at Gatwick Airport, West Sussex, before UK travellers from Portugal are required to quarantine for 10 days
‘While transatlantic links with the US are restricted, it’s costing UK economy £23 million each day. We urge Prime Minister Johnson and President Biden to lead the way in opening the skies, making it a top priority at the G7 summit.
‘Customers, families and businesses need to book and travel with confidence. After 15 months of restrictions, the time to act is now.’
It comes after the ongoing nightmare which has forced some Brits to pay through the nose to come home from Portugal early to avoid having to self-isolate after the country is placed on the amber list at 4.00am tomorrow.
To avoiding staying home, people are willing to shell out up to £1,000 to change their flights and Covid tests.
Green and amber list passengers who landed in Heathrow found that they were being forced to mix in queues while Border Force officials checked their Covid documentation and passports
British travellers pack out the departures lounge in Faro Airport, Portugal, as they dash back to the UK before tomorrow
Gabrielle Oliveira, 43, from Hayes, west London, who runs an aesthetic clinic, said: ‘I went to Portugal on Thursday and was supposed to be back tomorrow around 8pm with my two kids who are 17 and 18.
‘But because they have changed the rules, I decided to leave the kids there and come home, because I have work and it was too expensive.
‘I had booked my flight with Tap Portugal, but to change it was more expensive than to buy a new one.
‘So I ended up paying £500 for a new flight today and then an extra £170 for a last minute Covid test. It’s ridiculous because it’s the same test as we have at home except they write PCR in front of it.
‘I think it’s ridiculous to put Portugal on the amber list – they did it to make money on the football and then closed it again.’
UK arrivals from Portugal leave Heathrow Terminal 5 as they get home to avoid undergoing a 10-day quarantine
A health technician takes a nasal swab for a PCR test of a traveller at Synlab post in Lisbon Airport, Portugal
Ministers are not adding any countries to its so-called ‘green list’, dashing hopes that places such as Malta, Jamaica and Grenada could be added to the roster thanks to easing coronavirus rates
Sean Doyle, chairman and chief executive of British Airways, called on the men to ‘look to the science and base their judgments on a proper risk analysis’.
He said: ‘In the UK this means making the traffic light system fit for purpose, including a pathway to restriction-free travel for vaccinated travellers, and getting rid of complexity surrounding amber list countries, eliminating quarantine and reducing the number of tests passengers are required to take.’
Heathrow boss John Holland-Kaye said: ‘Connectivity between the UK and the US is one of the great engines of the global economy.
‘The scientific data shows transatlantic travel and trade can be reopened safely, and every day that policymakers delay puts jobs, livelihoods and the economic chances of hardworking folks across our countries at risk unnecessarily.
‘We cannot continue to keep locked up indefinitely.’
Race to escape the misery of quarantine: Frantic Britons queue for hours in baking heat in race against clock to get out of Portugal
From Gerard Couzens at Faro Airport
Frantic Britons queued for hours in baking heat yesterday as they tried to beat the clock to get out of Portugal.
Hundreds who turned up at Faro airport for rescheduled flights had to line up outside the terminal in 25C (77F) heat.
The wait was even longer for those scrambling to get Covid tests without which they could not get on their planes.
Those who fail to return home by 4am tomorrow will have to quarantine for ten days after Portugal was unexpectedly moved off the ‘green list’ last week.
Portugal’s downgrading triggered chaos as holidaymakers scrambled to dash home to beat ten-day quarantine rules which kick in at 4am tomorrow
This prompted many to cut short their holiday – some almost immediately after arriving – to go back home.
Algarve tourism bosses mobilised a lorry to beef up airport Covid testing after travellers were turned away from centres near their resorts.
Many decided to come to the airport a day before their pre-quarantine flights home to make sure they got test results. They took no chances after several holidaymakers missed their flights home at the weekend after failing to get their negative results back in time.
Katherine Hitchen, 30, from Hindhead, Surrey, travelling home with dad Michael and daughter Ivy, three, said: ‘We touched down on Thursday to texts saying Portugal had been put on the amber list. We were planning to stay for a week but are going back on Monday now to avoid quarantine.
‘It’s been a stressful few days since we arrived.
Katherine Hitchen with her dad Michael and daughter Ivy, three
‘I’d like to be sitting round the pool right now, not waiting to have a swab stuck up my nose.’
Louise Cooper, 55, from High Peak in Derbyshire turned up to be tested at Faro airport yesterday eight hours before her flight home. She said: ‘We got here on Monday morning and spent the first three days trying to sort out the tests for our flight home.
‘It’s been a nightmare. Everywhere was fully booked. The only place we were offered was a drive-thru in Faro which was about an hour away from where we’ve been staying in Praia da Luz. Being a drive-thru, we were told we needed a car – which we don’t have.’
Michael Nyhan, 70, who arrived on Thursday for a week’s break in Praia da Rocha with wife Angela, 67, said: ‘We’re going back today instead. We can’t face being cooped up inside again after the lockdown we’ve already been through.
‘We hadn’t even checked into our hotel room when we found out Portugal was going amber.’