there's one on Wooten Street near Waterloo that might have places. Coin Street is well regarded but they have a long waiting list. I've heard the Arc is good, not sure what story is with the wait list.
I think Bright Horizons at Tabard Square has spaces but it costs something like £350/week.
maybe do a search on childcarelink.gov.uk to see what else is out there.
no the one on Wootton Street is called Coral Day Nursery. I haven't been there. Have heard mixed things about Buffer Bear. My son went to settle in today at Lambeth Walk Day Nursery, which is sort of in the middle of nowhere but nearish to Lambeth North and Waterloo. Not sure I'm impressed, think we're moving though so it will be temporary (hope to get a nanny share instead). I also saw what I considered to be a decent childminder on Waterloo Road if you want to email me on firstname.lastname@example.org.
DH looked at Coral Day nursery once when we in were in a crisis about childcare. It was recommended to us by someone - can't remember who. He thought it was fine, not amazing, but fine. We went with something nearer to us in the end.