This place is worthy of more than a moment of your time - in fact it is worth much more than an hour, especially if you like the medium of film.
Head to the BFI along Southbank, perhaps stay for a beer if you like, especially if it's a nice day then you can sit outside. Then, when you're ready, you can take a stroll inside the building, perhaps stopping to pick up tickets for one of the films showing. Continue to follow the corridor around and watch as it slowly increases in size, opening out before you like an architectural version of Alice in Wonderland to reveal the heart of the British Film Institute, and its rather wonderful Mediatheque.
The Mediatheque is like a library from the future. There are no books, just lots of of booths and computer screens, with sockets for headphones (you don't need to bring your own, you go to the counter and book how long you want to use the Mediatheque for - the headphones are given to you at the start of the session). Then you get started.
Basically the Mediatheque is a catalogue charting the history of British TV and film, where you can book your time to see shows from across the gammut of entertainment, documentary and information programmes. Everything from commercials to feature films are covered, so whether you want to relive your childhood by watching the programmes you grew up with, or see a documentary you missed, it's all there for you to see. And best of all, it's completely free, now you can't say fairer than that.