Britain has so far only allowed very limited quarantine-free travel in recent months but the government has said that it will set out details of plans to allow fully vaccinated people avoid self-isolation on return from top destinations like Spain and France.
That rule change will come in by July 26, the first full week of the school holidays, The Times reported.
British business minister Kwasi Kwarteng said there were talks with EU countries to ensure travel could take place.
"We feel that the double vaccination does provide really, really first class support and protection against the variant, all the evidence suggests that, and we need to speak to EU governments and other countries to make that case," he told Sky News.
But on Tuesday, Transport Secretary Grant Shapps told the House of Commons that it was a “complicated policy that requires time to work through”.
It comes as millions of EU citizens will be given access to quarantine-free travel within Europe from July 1 after the launch of the bloc’s vaccine passport app.
But Britain is close to agreeing a deal with Brussels whereby its National Health Service (NHS) app would be accepted as proof of a double vaccination by the EU, and in return the UK would accept the bloc’s new digital green card for travel, The Times said.
All 27 EU nations, as well as Switzerland, Norway, Iceland, and Liechtenstein, are part of the green card scheme with Iceland not ready for launch after a recent cyber attack.
It is hoped the Government’s negotiations could avoid the recent confusion for Brits with trips booked to Malta turning up at the border to find authorities weren’t accepting the NHS app as proof of vaccination.
Travellers from the UK aged 12 and above are only permitted to enter Malta if they have had both doses of a coronavirus vaccine.
But authorities in the central Mediterranean archipelago revealed on Monday that they will only accept printed letters sent by the NHS as proof.
EU leaders including German Chancellor Angela Merkel have expressed their concerns at the number of cases in the UK and have called for tougher restrictions on British travellers.