The London Eye
This affordable tour gives you the luxury of spending as much or as little time as you want exploring the details. Take either the stairs or elevator up to an area with a 5 minute film explaining the history of the contest to design the bridge. Afterwards follow to the left to head to the glass floor viewing area. This area allows you to go to both sides of the bridge, with another short history film in between. The entire length of both sides has facts about how much the bridge cost to build, the types of marine life that live in the River Thames and compares other bridges around the world. After you finish the tower, head outside, follow the blue line and make your way to the engine rooms that lift the bridge up and down. Once you complete this part of the tour (optional) you can also head into the gift shop.
By far the neatest tour I have ever taken, from the end of July to mid September you are able to tour the staterooms at HRH The Queens official residence. At the beginning of the tour you are given a headset with a handheld audio/ video guide. Each room or section has a corresponding number to the guide. In this tour you see some of the royal families massive art collection, the different areas that HRH meets Presidents & diplomats, where official state dinners are held. You also get an inside look into how the staff prepares for such large events from the invitations, the menu, as well as different outfits she has worn. The tour takes about an hour or so and ends in the gardens where you can get coffee, tea, ice cream, etc. The garden area and the walk along the exit path is absolutely gorgeous.
IMO you can not come to London without experiencing all history housed inside Westminster Abbey. Like Buckingham Palace, you are given an audio set to take around at your own pace. Each are is numbered but some of this is a better harder to follow than the Buckingham Palace tour. You could easily spend the entire day looking at the different leaders, both political and artistic, buried here. The coronations have taken place here since the 1500's as have many weddings, Prince William & Duchess Catherine, and funerals, such as Princess Diana's. There is absolutely no photography allowed inside the abbey which definitely keeps people moving. Some of the spaces are rather tight and some dark. Take your time on this tour, it is worth experiencing as much as you can.