Many people get put off staying in London because of the price. It can be much more expensive to stay in a hotel but once you are there, there are some good ways of saving money. A lot of the art galleries and museums are free and so you can visit a lot of places without having to pay an entry fee. A bit of Internet research beforehand should help you to come up with a good list.
Public transport can be expensive as well but again it is worth researching this. There are many options, underground, taxis and buses and depending on how many people are in your party and how old they are, different things will be cheaper. It is also worth getting a good A to Z because you may be able to walk to some places which is a great way of seeing parts of the city and can save even more money.
Eating out in London can be very expensive. Even restaurants which belong to chains, tend to charge more than they do in other places. However, you can buy sandwiches from supermarkets which will save money and get takeaways.
Hotels can be very expensive as well. However, if you book in advance and stay off peak times you can get some good prices. It is worth watching the press for good deals or trawling the Internet as you can find significant savings if you look hard enough.
However, if money is not a problem or if you are happy with what you are spending, then there is so much to do in London that you will never be bored for a second. The atmosphere is quite different to other places in the UK, there is the mix of tourist and busy commuter which makes for an interesting bunch. Staying slightly outside of the city may mean that you get to meet more Londoners and feel a bit more of the real atmosphere rather than just that of the working city.