Boris Johnson will press Joe Biden to lift the ban on travel from the UK during talks at the White House tomorrow.
Britain dropped restrictions on fully vaccinated US visitors in July as a 'goodwill gesture'.
But, to the concern of ministers - and anger of the travel industry - the US has yet to reciprocate.
Mr Johnson and President Biden set up a dedicated working group in June to take the issue forward, following talks at the G7 summit in Cornwall.
But progress on the issue is said to have stalled.
Mr Johnson arrived at New York's JFK airport last night ahead of a meeting with the President
At present, travellers from the UK cannot visit the US without special permission from the United States government.
The ban meant that Tennis star Emma Radacanu's family were unable to travel to New York this month to watch her spectacular victory in the final of the US Open.
It has also deprived the beleaguered aviation sector of one of its most important and lucrative markets.
The US is continuing to ban travel from the UK on Covid grounds. But Mr Johnson will argue that the effectiveness of the UK's vaccination programme means there is no justification for maintaining restrictions on fully jabbed travellers.
British Airways chief Sean Doyle told the Daily Mail: 'The Prime Minister is doing something this week that remains out of reach for most Britons - visiting the US.
'We need the PM to urgently make the case for re-opening the transatlantic corridor during his meeting with President Biden and move the Atlantic Charter they discussed at the G7 back in June to the top of the agenda.
'For 18 long months friends and family have been separated and the UK economy has suffered.
'Aviation must be allowed to play its part in kick-starting the British economy, re-igniting business and tourism and re-establishing the crucial links we have with the US.'
The move to reopen travel corridors comes despite a SAGE scientist warning ministers are risking importing dangerous new Covid variants by 'abandoning' the testing system at the same time.
Professor Stephen Reicher, a member of the subcommittee advising on behaviour, said officials could have improved the system which saw 'absurd rates' charged for PCR tests by doing such testing through the NHS.
The traffic light system is to be replaced from October 4 by a single 'red list' of destinations, and those who are fully double-jabbed won't need a pre-departure test before returning from non-red list destinations.
From the end of October, they will also be able to replace the day two PCR test with a cheaper lateral flow test.
Speaking to Sky News's Trevor Phillips on Sunday programme, Prof Reicher said the system around PCR tests has been 'dysfunctional' with 'all the different companies charging absurd rates and not providing a service'.
He said the Government has responded to this 'not by improving the system but by abandoning it entirely', and added that, domestically, there remains 'huge uncertainty' about the effect on virus cases of the return of schools, universities, workplaces and people spending more time indoors in the autumn weather.
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