Just finished a visit to London with our twin 3 year old sons. Our stay at Ajit's flat was absolutely perfect for us. The location is fabulous, with lots near-by and along a very charming street and building. It was great to be able to put the kids to bed and shut the door and still be able to have some adult time in the evenings. We saved a lot of money by cooking our own meals in the fully ready kitchen (with grocery store only a very short walk away).
The only downside was the low level of soundproofing, but I think you'd find that in any of these charming London flats. Bring white noise for the kids if they're light sleepers and ear plugs for yourself.