Lola Rosa is a good I always think with kids in toe - food is child friendly and it keeps coming so keeps them interestd /happy /distracted!
Brinkeleys on Wandsworth Common is another fave of mine.
OR if you want to go north of the river for a change try Beaufort House - saw on NVN and its lovely. Had lunch with a friend there. Lovely spot - Kings Rd but the quiet end, fab decor and great menus - kids one too.
http://www.beauforthousechelsea.co.uk/
Now I'm hungry