Admittedly my experience is a good more than a 13 years ago, but I've never known anyone in London who used a fake id to drink. While the age at which one can buy alcohol is 18 (there's no prohibitions against drinking it, just buying it) it's so loosely enforced that it's generally just a matter of going to an off licence down the road if the first one asks for ID, so there's almost no point at all in getting a fake ID. Added to that is that there isn't any form of ID other than passports or driving licences which would have a data of birth on them, and an under 21 yr old not having either wouldn't be particularly unusual anyway.
I think things have changed a lot in the last decade or so in the UK in this respect. When I was at high-school we all went drinking in pubs from age 16 (with an 18 lower age limit); I genuinely doubt that's possible now given bar staff are supposed to challenge you if you look under 21.
As a UK national I can corroborate this :) I was the proud owner of a fake university ID (think it was from Heiot Watt) in my mid teens. Traded it by ripping some CDs with a first gen burner (which were still quite new in 1997/8!)