I think several people do them. If you see any mobile phone shops, you could just pop in and see, or ask at your hotel — I’d think a London hotel would know about that kind of thing.

I recently got a pay as you go SIM card to put in an old phone. I just went into a Vodafone shop & got a card for £10 with calls and some data that was valid for a month.

Here’s a page with some info: http://prepaid-data-sim-card.wikia.com/wiki/United_Kingdom