I know that London is more expensive to live in than the rest of the UK, but honestly I think you should be fine money-wise, especially if your husband will be working too.
My parents raised 3 kids on a combined salary of less than £35K (the youngest of us is now 16, the oldest, 23) and they spent a lot of money on our (well, mostly my brothers') sporting activities. One brother is a national gymnast, the other is a badminton player and my parents spent many weekends travelling the length and breadth of the country for tournaments and competitions. We could live comfortably on that salary and still afford the several hundred (possibly thousands of) pounds a year to fund the sports training/competitions/tournaments/travel, although we weren't in London.
Having said that, how much you can live on depends on what you are used to doing in the US. Life in general is more expensive here, so if you're used to going out to eat a lot, for example, you'll find that is it not as easy to do here without spending a fair amount of money. Because of all our other expenses, my family hasn't eaten take-out in about 10 years and we only go out for dinner maybe once a year (for a special occasion such as a birthday) - why spend £100 on a meal for 5 in a restaurant when you can save money and cook at home for £10
![Tongue :P](https://www.talk.uk-yankee.com/Smileys/classic/tongue.gif)
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