The Silver Screen Oasis

That's a clue.

Could it be Snatch (2000)?

Sorry, no.

Another clue: This movie was made at the tail-end of the British New Wave.

Nope, sorry.

Another clue: Cary Grant liked this movie.

Close but sorry, no cigar.

It's also not SATURDAY NIGHT AND SUNDAY MORNING.

Another clue: The title song for this movie was a hit back in the day, A lot of singers did their interpretations.

Alfie (1966)

Bingo!

Two young soldiers, clutching their guns, are sitting in a living room which is filled with modern art. The radio is playing a cantata. One of the soldiers rises and changes the station. A ‘40s dance tune plays. The two men dance together. The film ends.

Here is a rude guess as I have never seen this film, but have a hunchy hoo that it is Maurice.

No, sorry. Here's another hint:

Maurice is a lovely movie; the movie I'm going for here (despite the fact that it has been called a masterpiece) is by no stretch of the imagination a lovely movie, despite the rather poignant final scene.