Check out Simply Fabrics in Brixton. There are two shops, near the junction of Coldharbour Lane and Atlantic Road.
Otherwise, I tend to head to Shepherds Bush Market. There’s a bunch of shops on Goldhawk Road and in the market too. If looking in the market, check out the shops in the arches under the railway, which can be hidden from view by the market stalls.
There’s also a place in Tooting Bec called the Sewing & Craft Superstore, which has a wide range of fabrics, leathers (mostly offcuts / recycled furniture panels) and loads of other things. If you’re down that way on the first saturday of the month, there’s a sewing machine museum there that only opens 12 times a year!