First of all, in U.S. copyright, there is the educational exemption which allows (among other things) educators to screen films in their classes. But only in their class and for a pedagogical reason. You couldn’t screen it to the whole school or whole campus without having secured the public performance rights.
That being said, the university library where I work sometimes has two copies of a film, a regular ol’ DVD or VHS which you’ll find on the shelf and a public performance copy buried deep in the bowels of media services. If the student activities co-ordinator for the university wanted to screen King Kong, say at Freshman Orientation, (s)he’d have to make sure that the public performance rights were secured, even if a film professor was invited to make lengthy comments on the movie.
That being said, I’m a librarian and definitely not a lawyer.
I agree that the showing of the film must have an educational purpose, although I thought that went without saying.
However, I know of nothing in U.S. that prohibits showings of complete films, rather than just no more than necessary.
Gfactor gave the link to the U.S. code in post #5. Although the legalese is heavy, I don’t see anything there that forbids the showing of ordinary films in their entirety.
As I said earlier, national copyright laws do vary considerably in their fine details, and this provision may be different in the U.K.