http://www.saravanabhavan.com/
is really good South Indian vegetarian. I've seen an English family in there with children and I think they were regulars as the kids were picking out items from the menu themselves.
My personal favourite place in Tooting is Jaffna House which is Sri Lankan. The string hoppers with mutton curry is really delicious. Sri Lankan food tends to be very spicy though so you may have to be selective with children.
The Dosa places are good too and nice to have with mango lassi.
I am less keen on the Pakistani restaurants, but thats personal taste as they are very popular, but my children love the kebab rolls from Dawat as they are not spicy. Mirch Masala and Spice Village are always busy with families.
Chatkhara (North indian) is pretty decent too ( great biriyani) and they have a branch in Clapham South.
Veggie samosas from Pooja near Tescos are really crispy and moreish, but that is takeaway. Love those!