Boris Johnson has confirmed plans to open up quarantine-free travel to amber destinations.
Fully vaccinated travellers returning to the UK from an amber list country will no longer have to isolate on arrival.
On Thursday, Transport Secretary Grant Shapps will set out details of the Government's plans.
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Mr Johnson is said to favour easing the controls from July 19 - when other Covid lockdown restrictions in England are due to be lifted - according to The Times.
In a briefing from Downing Street, Mr Johnson announced that measures would be relaxed for double-jabbed arrivals, but the red list would remain in place.
He said: “We will maintain our tough border controls including the red list, and recognising the protection afforded by two doses of vaccine, we will work with the travel industry towards removing the need for fully vaccinated arrivals to isolate on return from an amber country.”
Heathrow Airport is to provide fast-track lanes for fully-vaccinated arrivals under a pilot programme to be launched this week.
On arrival at the airport, they will then be directed to dedicated lanes at the border to speed their passage through immigration.
Heathrow, together with British Airways and Virgin Atlantic - the two airlines involved in the trial programme - said it was essential that there was no delay in implementing the changes.
The scheme will initially involve fully vaccinated volunteers travelling on selected flights from Athens, Los Angeles, Montego Bay, Jamaica and New York.
Heathrow chief executive John Holland-Kaye said: "This pilot will allow us to show that pre-departure and arrival checks of vaccination status can be carried out safely at check in, so that fully vaccinated passengers can avoid quarantine from July 19."
His comments were echoed by Virgin Atlantic chief executive Shai Weiss who said: "To reap the benefits of the UK's world-leading vaccine roll-out, the UK Government must act now to remove self-isolation for fully vaccinated passengers arriving from amber countries, and no later than the domestic reopening on July 19.
"The UK is already falling behind US and EU and a continued overly cautious approach towards international travel will further impact the economic recovery and the 500,000 UK jobs that are at stake."
The call came after Health Secretary Sajid Javid announced people in England who have been double jabbed - as well as the under 18s - will no longer have to self-isolate if they have been in contact with someone who tests positive for Covid-19.
With cases continuing to soar, there were fears millions of people could be required to quarantine in the meantime, potentially damaging output just as the economy looks to pick up pace.
Mr Javid has acknowledged the numbers of new infections could rise to 100,000-a-day as restrictions come to an end.
Ministers are relying on the vaccination programme to protect people from becoming seriously ill with the virus and prevent the NHS from being overwhelmed.
