London - Family Restaurant Suggestions
Boxwood Cafe has come up before as a suggestion. It is a Gordon Ramsay offering in Knightsbridge with a children's menu that bills itself as child friendly. 3/5 stards from Time Out, so perhaps not the best out there, but kid friendly and is okay.
Locanda Locatelli is also reasonably child friendly (I've seen a couple when I've been there), not sure they have a children's menu, so you might want to telephone. Good Italian food.
My nieces have been taken to Roussillon, but I'm not sure they still offer their children's menu, and I've not been myself, but there have been posts on the board.
You might try going through some of the recent suggestions, and then checking on Time Out if they're listed as child welcome/child menu and then telephone or email to book and make sure.