Hello and welcome to the area !
Its so difficult around here as everything gets really booked quickly - when I arrived I seemed to be on every waiting list in SW11 !!! You could try Marmalade Cat on Battersea Rise .... you would definitely not be able to get a morning place (people put their kids name down at birth) but you could try for an afternoon place which would also give you the flexibility of doing 3/4 days (if you get a morning place you have to do 5 days). Eventually I got an afternoon place at Marmalade Cat - I could not recommend it more ! Its a fantastic nursery ! And I actually loved having an afternoon place - our mornings were so relaxed. They also have a nursery in Balham which might not get so booked up ? Its run by the same lady so I am sure it will be just as amazing as the one in Battersea Rise.
This is the one on Battersea Rise
http://www.marmaladecatschool.co.uk
This is the one in Balham
http://www.caterpillarnursery.com/
There are a lot of other great nurseries in the area. You could also try Mouse House and Sparkies? You will have the same problem with Mouse House (i.e. unlikely to get a morning place). I don't know much about Sparkies apart from the fact that a few friends have kids there and really like it.
Good luck !!