Okay, a bit of feedback:
Art Veneers - Haven't had cause to use them for about 15 years, but when I did they were helpful, the order was well packed and no complaints whatsoever. I would guess better for the marquetry fraternity than furnituremakers wanting consecutive leaves of rare burls or whathaveyou though. Excellent catalogue - more of a veneering handbook than a price list.
British Hardwoods - I've used them repeatedly and have had consistantly good, clean sawn and planed boards from them. They also err on the side of generosity to allow for any small areas of knots and so forth in my experience. Waney edged stuff not so hot; that's based on a sample of one order but also my gut feeling is they prefer to send s/e stuff by mail order. Their one serious failing is delivery; the last order was to be "ready in a fornight", but only turned up a week later after some serious prodding. They've also been known to send off an order without warning and it just turning up unannounced. On the other hand the rate for delivery of s/e boards is a flat £15 + VAT, which is very good. Buying timber sight unseen isn't ideal, but BH have proved to be the most reliable method to do it.
South London Hardwoods - Years ago now I bought one of their pallets of off-cuts. Delivered okay, timber not bad but an awful lot of 3/4" square sticks of woods which I'm still working my way through. I've not ordered from them subsequently mainly because of the rather hefty delivery charges - the wood itself was okay.
Cheers, Alf