I am going to London with my 13 year old son and 9 year old daughter in August. They, of course like interactive things. I would like all types of suggestions for kids this age. Thanks.
The Science Museum in South Kensington has all sorts of great interactive exhibits.
The Natural History Museum, which is conveniently located right next to the Science Museum.
The Museum of London.
V&A Museum of Childhood.
A few weeks ago we were at the animatronic dinosaur exhibit at the Natural History Museum, which appears to be a popular attraction for London families. Suggest trying to go during the week, weekends are when London residents take their kids so there are long lines.
All the above are good. Plus the London Transport Museum in Covent Garden.
The Tower of London is great for kids, especially if you see the Crown Jewels as well as the military stuff. I took a nephew and niece a few years ago, and they enjoyed it. It's not exactly interactive though i.e. nothing much to press or poke.
London Zoo would have been an attraction at one time, but don't interact with the lions. It has gone posh now and refers to itself as ZSL.
The V&A Museum of Childhood in Bethnal Green has a number of activities every day, but possibly your son might be a bit too old for these. The exhibitions though have been completely refurbished in recent years, although are fairly static.
Another vote for the Museum of London and for something completely different check out Mudchute farm. http://www.mudchute.org This link might also help you find other places of interest for them. http://www.dayoutwiththekids.co.uk/things-to-do-family/Greenwich/Museums-and-Galleries
We visited London several times when our boys were growing up. Here's some of the things they and we enjoyed doing:
Thames River cruise, War Rooms, British Museum mummies and Rosetta Stone, Tower of London, riding on top of a double decker bus, Harrods toy department followed by lunch at Zia Teresa across the street (became a ritual), climb to top of Monument (good exercise and London views on top), West End plays, Natural History Museum.
We went to Westminster Abbey around Christmas time when it was almost devoid of tourists but don't know how it is in peak tourist season. My older son showed more of an interest in people like Sir Isaac Newton and Charles Dickens buried there. We also went to Peter Pan statue in Kensington Gardens but I think our boys were younger then than your children are now.
The London Eye was built after our family trips finished but it's fun for all ages.