There is indeed a record fair in Olympia (a short walk from Earl's Court station) but that is on the 24th so your friend might miss that. This site lists most of the record fairs: www.vip-24.com
As for record stores. I'll start with the chain stores.
Probably the best would be HMV on Oxford Street, The best all round selection at the moment which spans all area's. They usually have a good selection of back catalogue and their rock n roll sections (i.e. early rock n roll) is great. Also has vinyl.
You can also hit Zavvi on Oxford St & Tottenham Crt Rd corner. There is also a Virgin at Picadilly Circus. I haven't been there for years but I think the selection is still very good. Yo ualso have Fopp just down the road on Tottenham Crt Rd which sells new stuff and has great prices on back catalogue cds. Think Â£5 range (with the USD to Â£ exchange you should get some good deals).
For non-commercial shops head into Soho. On Berwick St you have Sister Ray a used record store who's name escapes me a few doors down and a bit further down you have Music Exchange which is another record store. There is also a shop called SOund of the Unvierse but that deals mainly with non-rock stuff.
Just off of Oxford St is a Hanway which has two used record shops that sell mainly collector vinyl. Nice shops but haven't been there for ages.
All the shops above are basically within walking distance from each other. Very close.
Ouside of Soho you got some shops as well. If you're friend can make it out to Spitafields he should have a look at Rough Trade. You won't find regular rock stuff (I'm not even sure they stock Zeppelin to be honest) but if you want newer music its the place to go. Lots of electronic, new folk, etc.
In Portobello Road there's a shop called Intoxica: http://www.intoxica.co.uk/
I went there ages ago and they had a lost of collector vinyl.
I think there is a Music Exchange not far from Intoxica in Notting Hill. That used to be very good.
I've lived here for 14 years and yes the selection of record stores has drastically reduced. Soho used to have a lot of them but the selection now is still good. It could be a lot worse!