I saw the (very bad) 2000 American remake starring Brendan Fraser and Elizabeth Hurley quite a few years ago, but I wasn't aware there was a British original until quite recently.
Stanley Moon (Peter Cook) is a short order cook at a café. He's in love with the waitress Margaret (Eleanor Bron), but too shy to do anything about it. Unhappy with his life, he tries to commit suicide, but fails even in that. And then George Spiggott (Peter Cook) walks in and explains that he's the devil and he'll grant Stanley seven wishes in return for his soul. It takes a bit of convincing for Stanley to believe it, but he takes the deal.
What follows is a sequence of wishes gone wrong: Stanley keeps trying to get together with Margaret, but in every case some element of the wish goes terribly (and comically) wrong. And as he accuses the devil of deliberately sabotaging his wishes, the two of them develop something resembling a friendship.
Cook and Moore are both quite good. Like its later remake, it lost a lot of emotional weight by being so incredibly absurd in places - although it was also pretty funny because of some of those ridiculous interludes. It still manages some good whacks against Christianity.