Those I've done business with.
http://www.handyhippo.co.uk/ - These guys came up in searches again and again for paper and card supplies. They have a very well-designed website, a good range of card, paper and embellishments, are reasonably-priced and delivery VERY quickly.
http://www.craftingdirect.com/ - Essentially a wholesaler/catalogue shop. When you register with them you'll get a store card but provided you pay the invoice as soon as they send it (a few days after my purchase, in my case) then you don't get charged. The interest rates are pretty hefty for failure to pay balance though. I'm also getting clothing catalogues through my door from their parents company, JD Williams. :/ That said I found some brilliant paper at an excellent price!
Here are some I've bookmarked but didn't order from.
http://www.weddingcrafter.co.uk/ - all the supplies for making fairly traditional wedding invites
http://www.craftystuff.co.uk/ - Lots of crafting and paper supplies including wedding-specific
http://www.telfordsdirect.co.uk - Some nice funky paper and in packs.
http://www.craftsite.co.uk/ - Some really nice embelishments. I loved their paper flower packs!
I can't vouch for any of the above but they all seem pretty decent shops. Hope this is helpful to some of you!