the willows saw mill is good for oak but its green but they have oak air dried and yew and London plane its just outside Uckfield I too am in Eastbourne The willows are very reasonable on price.
Morgans have an excellent selection. however if you just turn up the prices they charge I think they believe they are selling solid gold as opposed to timber, Caveat emptor
We went to Morgans since it was so close to our friend' house! They were nice and helpful and the wood was suuuper cheap, compared to what I'm paying at Alsford timber. BUT I forgot most of the reason I need a new supplier is so I can choose my wood, and I forgot to, and 2 of the 3 pieces I bought have cracks....
I need a closer place though, I'll check out The Willows.