The relaxation would initially only apply to UK residents with access to the NHS, but a deal to extend it to all EU citizens is reportedly "close" to being signed, according to The Times.
UK ambassadors in Europe are said to have been told to make lobbying for the lifting of restrictions on British holidaymakers a "priority".
"The big focus for us is Europe now... all European ambassadors have been told to go and lobby," a government source told The Times.
