Boris Johnson is expected to push for the lifting of a ban on travel to America when he meets US president Joe Biden in Washington this week.
If successful, it is hoped the restrictions imposed on travellers from the UK could be abolished within two months.
Both leaders pledged to take action by creating a taskforce when they met at the G7 summit in Cornwall in June but so far little to ease transatlantic travel curbs to the US has materialised.
Airlines such as British Airways and Virgin Atlantic are desperate for a transatlantic breakthrough to allow for the resumption of travel freedoms on lucrative key routes such as London-New York.
Carriers believe that the US travel ban first imposed 18 months ago could be lifted in November, just ahead of the Thanksgiving holiday, paving the way for Christmas breaks.
The UK relaxed its restrictions on US citizens at the start of August, allowing double-vaccinated travellers to enter without quarantining for ten days. Further restrictions, including the need for a PCR test, will be removed for those who are double jabbed entering and leaving England next month.
Downing Street said that the prime minister saw his visit to the White House on Tuesday as an opportunity to discuss how to reopen international travel.
Johnson will also have an opportunity to put UK-US travel on the broader Washington agenda in meetings with vice-president Kamala Harris and congressional leaders from both parties, including Nancy Pelosi and Mitch McConnell.
A senior government source told The Telegraph: “The prime minister will make an impassioned case for Brits who’ve been double jabbed to be allowed to travel to the US. There are a lot of family links, business links and millions of tourists usually travel every year.”
In a normal year more than four million Britons fly to the US annually, but only a fraction of those trips have taken place during the pandemic and tight US restrictions.
Airlines UK chief executive Tim Alderslade told The Times: “The US is one of our most indispensable markets, worth billions every year to both countries in trade and tourism.
“Our exports can never reach their true potential as long as this key air link remains closed to British companies, and we urge both governments to redouble their efforts to reach an agreement as quickly as possible.”
New foreign secretary Liz Truss is joining Johnson on the visit, marking her first international trip in her new role.
The Foreign, Commonwealth & Development Office (FCDO) said: “Discussions will focus on G7 priorities and climate change in the run up to COP26.”