In Southfields The Gardens Childcare group have 2 nurseries, one on Revelstoke Road called The Litte Hall, which is not too far from Earlsfield, and then they have another one closer to the tube station towards Wandsworth. The Little Hall is great, the team are all so loving towards the children but they do have a long waiting list. However, we had to wait more than a year to get a place, I registered before my son was born!
You may have to go for a childminder until a nursery place opens up. Both Wandsworth and Merton councils maintain lists of registered childminders and will send you the details of people near you. Also there is a group from a Wandsworth Childminding Association who meet from time to time and they usually post details on this website of their next meeting - you migth meet some childminders there and they also maintain lists of registered childminders. Finally you could try
www.*********. Its free to register and then take a look and see if there is anyone you'd want to contact, but to actually contact anyone then you need to pay about £15 for 3 months to be able to contact people through the site. I used this site to find a temporary childminder until my nursery place came available.
Good luck.