The risk-based system with red, amber and green ratings for different countries, determines the quarantine and coronavirus testing requirements people face when returning to the UK.
The legal action will call for greater transparency over how Whitehall decides which countries qualify for the green list, the BBC said.
‘They’re making this stuff up as they go along’
Ryanair boss Michael O’Leary has said the “stop, go, stop, go approach to travel is bonkers”.
He told Sky News: “It’s typical of Boris Johnson’s Government, just making this stuff up as they go along.
“There is no green list.
“What we keep calling for in the travel industry is, now that we have 80% of the adult population of Britain vaccinated, why can’t those people go on holidays to Portugal and Spain without restrictions? They’re already vaccinated.”
An industry body warned on June 9 the “failed and damaging” system for international travel must be abandoned if the UK travel and tourism sector is to be saved from total collapse.
The World Travel and Tourism Council (WTTC) said the Government must scrap the system, which has “wreaked havoc” among consumers and businesses, in order to save hundreds of thousands of jobs.
Travel plans for people who have had both vaccinations
It comes as officials consider proposals that could allow Britons who have had both coronavirus vaccine doses to avoid having to quarantine when returning from countries on the amber list, according to reports in The Daily Telegraph.
A Government spokeswoman confirmed work had begun to “consider the role of vaccinations” for inbound travel following the continued success of the jab’s rollout.