There's one called Cycle Revival in Heathfield
http://cyclerevival.co.uk/
Haven't used it often enough to be able to recommend it but it seems adequate.
There's also a shop in Robertsbridge which doesn't seem able to decide if it's a classic motorbike shop or a bicycle shop. Haven't used this at all so couldn't say if it's any good.
Depending which part of East Sussex you're in, you might be able to get to Tunbridge Wells, which had at least one bike shop at the last (pre-credit crunch) count.