This has always been a bit of an annoyance to me. The idea of a typically British film. What immiediately springs to mind are some of those mentioned here like Brief Encounter or the Ealing comedies. But what about films like The Long Good Friday, Performance or Trainspotting, more recently Dog Soldiers and so on.
Brief Encounter is one that would be classed as "quintessentially British" due to the stiff upper lip characters, and the chaste storyline, but i feel this is due more to foreigners' view of Britishness rather than how the average Briton views themselves.
Also, a typical British film seems to contain upper/middle class characters because these are the people who tend to make them