Silverbrooks
The chronology of swearing in films is well documented.
The f word began to break into British cinema when it was uttered once in the film Vapor (1963) and in two Andy Warhol films – Poor Little Rich Girl (1965) and My Hustler (1965), and later in each of two 1967 British releases, Ulysses and I'll Never Forget What's'isname. It was used several times in the 1969 British film Bronco Bullfrog.
It certainly wasn't commonplace.
I doubt that the Andy Warhol films count as “British” cinema -
Vapors is similarly an American film, a 1965 short film directed by Andy Milligan and written by Hope Stansbury. The film portrays the lives and conflicts of a group of gay men set during one evening in a New York bath house for men.
Vapors
Directed by
Andy Milligan
Written by
Hope Stansbury
Produced by
Andy Milligan
Cinematography
Andy Milligan
Edited by
Andy Milligan
Running time
32 minutes
Country
United States
I have yet to find out about the others.
TBH I have no recollection of films in the 1960’s using this phrase and find it hard to imagine it being enunciated by the actors or film stars of the day 