I'm reading Alan Bennett currently for a book group and found clips from many of his TV plays on Screen Online, produced by the British Film Institute. There are a huge number of other clips from other British films and television productions on there too - for example 'Great Expectations' (1946), 'Trainspotting' (1996) and 'The Office' (2001-2003).
There are also some full-length films such as Karel Reisz's 'We Are the Lambeth Boys' (1959) and Shane Meadows' short film 'Where's the money Ronnie!' (1996).
You can search Screen Online for your favourite British director, actor or film etc or browse for films grouped by genre, theme, place or decade. There are also 'tours' of themes such as 'Cinematography,' 'Britishness,' 'the British sense of humour' and 'writing short films.'
It is a wonderful resource for film students or for anyone interested in film!
Much of the text on Screen Online is available to anyone on the Internet, but you have to be within a school, university or public library to view the clips.