I don't know if they're free or not, but I've been to functions in the Earl Spencer (a christening reception thing) - it's a really nice pub, great food, on Merton Road; and also at the County Arms, which is on Trinity Road, right opposite Wandsworth Common. They do good food too, have a lovely garden, an upstairs room, and the Common is really handy if little ones need to go and have a run around!
Have a great birthday party!