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The US will relax travel restrictions and admit fully vaccinated passenger from the UK and the EU.
The White House said it will end an the 18-month ban on foreign travellers entering the country from November.
It comes as UK Prime Minister Boris Johnson met US President Joe Biden at the White House during his visit for the United Nations General Assembly. Pressing for the travel ban to be dropped was on his agenda.
The relaxation will now bring the US more into line with the UK, which in October will introduce a new set of travel rules for England, scrapping the travel traffic light system in favour of simpler measures and less testing.
Former US president Donald Trump imposed a blanket ban on travel at the beginning of the Covid pandemic as infections and deaths rose sharply.
The news was welcomed by Mr Johnson, who described it as a “boost for business and trade".
British Foreign Secretary Liz Truss said the news was important for “economic recovery, families and trade.”
The announcement is a major boost for airlines such as British Airways and Virgin Atlantic, and Heathrow Airport.
They have repeatedly blamed the travel ban for limiting the recovery of passenger numbers during the virus crisis.
Shai Weiss, chief executive of Virgin Atlantic, said the easing of restrictions is “a major milestone to the reopening of travel at scale, allowing consumers and businesses to book travel to the US with confidence”.
He went on: “The UK will now be able to strengthen ties with our most important economic partner, the US, boosting trade and tourism as well as reuniting friends, families and business colleagues.”
Heathrow boss John Holland-Kaye said: “Connectivity between the US and the UK is part of the bedrock of the global economy.
“The Prime Minister has secured a massive win for global Britain in getting these links restarted.”
About 3.8 million British nationals visited the US every year before the pandemic, according to the Foreign, Commonwealth and Development Office.
The reversal of the measures comes only weeks after the UK government began to allow fully vaccinated passengers from the US back into the country.
Diplomats across Europe, as well as the European Commission, have for months been piling pressure on Washington to scrap the travel ban, which they argue is unjustified.
The current rules stipulate that only US citizens, their immediate families, green card holders and those with national interest exemptions can travel to the US from the UK or EU nations.
It comes as UK’s Transport Secretary Grant Shapps said Britain’s aviation industry stands to “absolutely” reclaim its pre-pandemic status.
Airlines and airports say the government’s quarantine and testing rules have restricted their recovery from the Covid crisis and are calling for more restrictions to be eased.
Heathrow has gone from being Europe’s busiest airport in 2019 to its 10th busiest, behind rivals in Amsterdam, Paris and Frankfurt.
Industry body Airlines UK said the UK’s aviation network was behind only the US and China before the pandemic.
Asked whether the sector would recover, Mr Shapps said: “It will. Absolutely.”
He said the UK would “not only get flying again”, but was also “leading on decarbonising aviation as well, which is a huge challenge”.
Mr Shapps said rules for international travel announced last week would move Britain towards “the more normal world of travel, which is that when you’re fully vaccinated you will be able to travel”.
“That relies on other countries doing the same thing,” he said.