Airlines are calling for a relaxation of the rules for those who've had both doses, and today officials are discussing whether that should happen.
British Airways, Heathrow and Virgin Atlantic held a pilot scheme with around 250 fully vaccinated passengers presenting their COVID status.
Only two were turned away, one due to an identity issue, and one because they were vaccinated less than 14 days before travelling.
Heathrow boss John Holland-Kaye says "There is now no reason to delay with rolling out the solution from July 31."
Joss Croft, from the tourism trade association UK Inbound, says American holidaymakers are crucial for the UK's economy.