We went last year with a 4 & 5 year old, My advice is don't try to cram too much in. You can always go back next year.
For info, our day was:
Tube from Stanmore - youngest really wanted to go on the train but it cost loads and this was a good alternative.
First stop Hamleys, looked at the whole store, gave them a £30 budget for toys, this was more than adequate.
lunch was not planned - oversight on our part, we ended up at 5 guys, but I'd advised booking into the Rainforest cafe or Planet Hollywood type place. much more exciting for kids and better menus and probably similar money.
Shrek's adventure tour - this was brilliant, the kids loved it and the staff were great. It was also a great walk there as we passed Big Ben and the HOP.
Walk along Southbank, seeing the buskers, one had one of those giant bubble things and they loved it, there's a great park there to, ice cream stands etc.
Dinner at a restaurant nearby, I can't remember the name of it, but it was about a 7 min walk from the park at Southbank and was great for kids.
back on the tube to Stanmore, Pj's on in the car, around an hour's drive home where they both fell asleep having had a lovely day.
We walked and tubed everywhere, with the giant buildings, busses, statues and shops, there's plenty to keep them distracted from a longish walk, we did buy a bit of tat from street sellers as they distracted them, but only a few pounds and kept them occupied.