My friend and neighbor is on the board of The Small Project. Nice people, good organisation.
From their facebook:
Hi. The Small Project collects good quality second-hand baby clothes and equipment and passes them on to local families. We're based in Kennington, south London. Families in need of items can be referred to us by health/welfare sector workers. Please get in touch if you'd like to refer, be referred, donate or just find out more -
info@thesmallproject.org.uk
https://www.facebook.com/thesmallproject/?fref=ts