I visited London with my daughter a couple years ago. I'd highly recommend researching the attractions you might want to see and purchasing your "must do" tickets ahead of time. For instance, you can get tickets for SeaLife (formerly known as the London Aquarium), the London Eye, Madame Tussaud's and the London Dungeon all packaged together for one price. (Check out
www.thedungeons.com/london)
Then, once you've figured out your "must do"s, you can start to pull together a touring plan. For instance, the London Eye, the London Dungeon and the Aquarium are all right next to each other, and you can quite easily spend the entire day checking out all three.
Madame Tussaud's is near Baker Street, so make a great pairing for another day. Also, the London Museum is nearby (although personally I could spend days there!).
The Harry Potter Experience at Warner Bros Studios is a great deal of fun, but is a bit tricky to get out to if you're not used to navigating the trains. This is another one you'll need to purchase a ticket for, in advance, online.
The Tower of London is well worth seeing. Take your time and be sure to sit in on some of the presentations and tours ongoing throughout the day. As well as see the crown jewels! I considered this one a full day experience, but it really depends on your touring style. I like backstage-style tours and always sign up for whatever's available.
Find yourself a centrally located hotel near a tube station, and plan your routes on the underground ahead of time. You'll feel a lot more confident, if you know where you're going. We stayed at the Best Western Victoria Palace near Victoria station and got a great room rate, because we booked very early.
And, just like you're visiting Disney, you'll be fighting crowds, almost all year around. So, unless your pre-purchased ticket has a specific time on it, be sure to show up at least 20 minutes before the attraction opens.
By the way, you don't have to visit a specific attraction every day you're in London. Just exploring on your own is a great deal of fun, too. Walking around we saw the guard change at Buckingham palace, found Princess Di's memorial garden, saw people riding horses in the park, discovered a bookstore full of such rare old books that the proprietor had to buzz us in past a locked door to see them and ate at a cool restaurant where you ordered on your interactive table/screen.
Also, don't forget to take in a play, if you've got time! We saw Wooster and Jeeves in an immensely old theatre.