Not sure about SE1, but I'm told that there's a magical emporium at the top end of Lavender Hill, called something like Fabric World/Fabric Wonderland/World of Fabric, and it stocks everything you could ever want. I'm sure it's got "Fabric" in the name, anyway. Apparently, it's quite a long way up the road, away from Clapham Junction.
Mrs I went there one day recently, and came back with an expression of such elation that it took me back to the days when we were courting.
Otherwise, it's a tube ride to the 4th floor at John Lewis, perhaps?
If you find anywhere local, please put it up on here, and I can earn great kudos with Mrs I.
Great tip, Eileen (Kleins). I see they do suspender clips and "specialist boning". I will do my best to get Mrs I round there at the earliest opportunity. You never know, I could recover my lost youth yet....;0)
A bit further out, in Lewisham, is Rolls 'n' Rems who do very cheap fabrics, haberdashery and dress patterns. I go there because they also do DMC embroidery threads (quite hard to find these days. The shop is very cramped and usually quite crowded, but it has character!
A fabric stall at the E&C would be great, wouldn't it!