For felt, fleece, etc for plushies / softies, I found that "Rolls and Rems" in Holloway was very good (21 Seven Sisters Road). They had a large amount of other fabric in the store, too, of course.
The only things I couldn't get there while assembling a basic starter kit were: some embroidery thread+needles, a sharpie.
Felt squares were priced standard rather than cheap: 45p a square, with a selection of maybe 25 colours. I think they had some on rolls as well, but can't be sure. I guess you can call them.
As a newbie, I also found the staff helpful.
Here's their site:
Looks like they have three stores in total:
111 High Street, Lewisham, London, SE13 6AT
21 Seven Siters Road, Holloway, London, N7 6AN
9 The Concourse, Edmonton Green, London N9 0TY
A girl in walthamstow market told me about this place when I asked her where to buy felt ( I didn't find any felt anywhere in that market, but didn't look exhaustively).