Without in any way trying to dissuade donations to the organisations already mentioned, Hestia is a domestic abuse centre, among other things, that operates in Wandsworth and elsewhere. They've (sadly) been around for 40 years and seem a good place for clothes and toys. I gave them a big bag of baby clothes to them last week, and they'd be very happy to receive donations. They can't always take things and around the holidays are flooded with toys, but would be grateful for clothes pretty much any time, and happy for toys much of the rest of the year. email@example.com
or 0208 871 2664. They kindly collected from me, in Balham.