You're in for a treat, London is a fantastic city. For budget, do you have a particular amount you'd like to spend for the week? It's best to get an idea of how much you can spend/afford, convert it to Pounds and go from there. Every person on this site has a different budget in mind when they travel. I like to budget high for any unexpected expenses or just to say "I was under budget" at the end of the trip. If your hotel provides free breakfast, that's a great start. Depending on when you go, a cheap and memorable lunch can be a picnic in the many parks. My favorite part of London was buying sandwiches in a local grocery store and sitting in the park in front of Buckingham Palace surrounded by tulips and eating lunch.
It's been a few years since I've visited London, so fares may have changed. I'm sure there will be a few additional posters who can help you out with a more accurate approach to the cost of museums and transportation. My advice though, don't bother with the Hop on Hop off bus tours if you can help it. Although comfortable and a great way to see the city, they are terribly expensive.