Fabric Shack has loads and loads of fabric at really good prices (especially with the current exchange rate) and their shipping is fast and cheap - my order arrived here in NZ a week after I placed it. The downside is that their website is not that well designed so it is quite time-consuming to browse the fabrics.
Reprodepot has loads of lovely fabric as well and is much easier to navigate, but it's not quite as cheap.
Unfortunately I need fabric in the next 24 hours to make a Thomas the Tank outfit for Fred for World Book Day (think cyan cotton!) ... so first port of call in the morning is John Lewis with Berwick St if no luck there!
Sorry this is too late but I can confirm there is a fabric shop in East St as Dee Dee suggests - it is a fair way down the street away from Walworth Road on the south (right hand in that direction) side, but before Portland St, almost opposite the end of King & Queen Street.