The Quash Quarantine group is holding off the threat of legal action after being assured that air bridges to low-risk countries will be introduced from the end of the month.
The collective of 500 travel and hospitality companies indicated that its legal move against the government's restrictions on international arrivals into the UK imposed on Monday would be paused.
The group's spokesman Paul Charles said: "We've received private assurances from senior government sources that travel corridors will be in place from 29 June.
"We urge the government to signal to the travel industry publicly and urgently that this is the case, as well as amend FCO advice on non-essential travel.
"We are still considering our options regarding legal action, including whether to join BA's claim, but would prefer that 29 June is confirmed for the start of travel corridors."
Portugal, Spain, France, Italy, Greece and Australia are believed to be frontrunners for "travel corridors", which would allow holidaymakers and business people to go to and from the countries without having to self-isolate for 14 days.
Confirmation could come this week after the Cabinet meets today (Tuesday).
It is likely to be allied to a lifting of the Foreign Office ban on non-essential travel to "low-risk" countries after the advice was marginally amended yesterday.
The quarantine still faces a legal challenge from British Airways owner IAG plus rivals Ryanair and easyJet.
Ryanair chief executive Michael O'Leary said the bid for an injunction could be heard by the end of the week.
He said: "I think the courts will hear it quickly because it is an injunctive-type measure.
"We don't see how the Home Office will be able to put up any defence whatsoever. There is no way that they can argue in court that this is an effective quarantine or that this has any scientific basis at all.
"It is an irrational measure that does untold economic damage to British tourism, to millions of jobs in British tourism.
"It seems to be having very little impact on British people going abroad in July and August – they are already booking in their hundreds and thousands."
By Phil Davies