The Great Escape (1963), directed by John Sturges.
Misc notes:
In the opening scenes, Elmer Bernstein's whimsical score clues us that this will be a fun, "cozy" war picture, exciting but not too serious or gruesome. It darkens in the final act when a bunch of our escapees are shot, but comes back with Steve McQueen bouncing that baseball.
The prisoners are all on a first-name basis, unusual in British Army pictures.
The July 4th moonshine scene is especially fun.
This is a The Magnificent Seven (1960) reunion, with Steve McQueen, James Coburn, Charles Bronson, the director, producer, composer and other crew.
Actor James Donald, the Senior British Officer, deserved some sort of award for POW films: he was also in King Rat (1965) and The Bridge on the River Kwai (1957).
Screenplay by James Clavell, who also wrote King Rat (1965).
Available on Blu-ray. I don't remember seeing this on film so can't be sure what it is supposed to look like, but the Blu-ray verges on the ugly. Detail is usually poor, the image dim and the colors washed out.
Later: I've replaced the thumbnails with images from the Criterion Blu-ray. This is a good upgrade but the film is never going to be spectacular looking.