Any of the chains are good - Bills etc - bit the food can be a bit boring.
The French Kitchen on Trinity Road does great food and I know in the past they have pitched menus at kids - I haven’t been in there for ages though. That’s where I would go for a “proper” lunch with little ones.
The other one is the chicken shop by tube in balham - mine love it and it feels a bit less cookie cutter than the usual chains.
I would avoid Ben’s Canteen in Earlsfield with children, I visited with a friend and two of our children in late July and the waitress in there was very rude - covering her nose as we paid because the youngest child needed a nappy change (plan was to pay then sort that out, and we were the only customers in there), and when we got back upstairs after nappy change to leave the waitress was moaning to her colleague about having to clean the highchair that the 10 month old had eaten at saying “this is disgusting”. My 3 year old even noticed her bad attitude throughout and (asked me in front of her!!) “why is she angry”.
If you want a special treat (as it’s quite pricey), then kids love Good Earth on Bellevue. It’s not the sort of place where they can run around or be noisy but they love the food. If you go early evening it’s full of families celebrating birthdays or other special occasions.
Also there’s a fab gelato shop in Earlsfield called Cremoloso Gelato. It’s owned by a guy from Milan who makes the ice cream on the premises. Well worth a trip.
I can HIGHLY recommend Numero Uno on Northcote Road - we took my 14 year old niece there on friday night (at very short notice having been turned away from an establishment booking down the road). The welcome was lovely, we had a lovely big round table for the 6 of us, the food fantastic and service excellent. You might want to give them a ring to check their booking policy for children though...see my other post today. Enjoy!