Depends on where you'll be.
Good idea to buy a copy of MIniworld or Mini Magazine and just browse the adverts to see where things are and what they sell
You'll get a lot of opinions as to who's good and who's bad, i'd say the concensus is that Huddersfield Mini Spares are cheap - but cheap for a reason. We had some spot & fog lights from them that were very cheap at a mini show but were peeling the 'chrome' within months.
Apparently they are much better if you are shopping in person, but notorious for poor customer service when items are bought at mini shows or by mail order.
Mini Spares Centre have got huge stock, they remanufacture parts from original tooling and therfore have some unique parts that you can't get anywhere else. They also have 3 locations across England, so you stand a chance of being near one. Their main warehouse is just outside London in Potters Bar.
They also tend to have very knowledgable staff in my relatively limited experience (maybe 3 or 4 purchases over 5 or 6 visits).
go to
http://www.minifinity.com
... and go to the forums for some UK users advice, I think you'll find threads on most of the major suppliers, with good and bad stories for all but I guess it depends on what you are looking to buy.
I think the better places for pre-browsing on the internet for parts and accessories are:
http://www.minispares.com
http://www.minisport.com
http://www.plmini.com
I had a mate when i lived in Scotland who swore by P&L Minis (they're based in Yorkshire), he always got his stuff from them and never had any problems. They've got a very extensive website shop but beware of the spelling of many items if you're doing a search - I bought a set of John Cooper Signature decals this week which were listed as 'John Cooper Signuture', just an example but you see what i mean!