I second the Falkirk Wheel in Falkirk, Scotland. There is a fantastic and inventive water play area next to the water wheel (which I don't think kids would find interesting after a few minutes; it moves slowly). You can also go for a walk into the woods there along the John Muir Way, and see part of the Antonine Wall.
We also loved Doune Castle, a short drive from Stirling. As it is partly a ruin, kids can roam around stairwells and passageways. There are paths from the castle through a lovely park to a nearby river; you can also walk into town via the site where a Roman fort was and have lunch in the charming village. (An aside: we had a nice chat with a sweet Scottish lady at the café who told us she cried when she saw the Golden Gate Bridge earlier this year.)
What else did our kids like at that age ... doing things, like taking the boat to Greenwich and seeing Harrison's clocks and the maritime museum; attending evensong at Westminster Abbey; the transport museum at Covent Garden; the Ceremony of the Keys at the Tower of London; rambling through cemeteries, such as Highgate and Bunhill Fields; the Cabinet War Rooms; exploring the HMS Belfast; interactive exhibits at the Imperial War Museum (& the playground outside!); re-enacting the Battle of Hastings (just by ourselves) at Battle Abbey; throwing rocks into the sea at Pevensey Bay; Dover Castle, including the secret tunnels; Portsmouth and its ships; Bodiam castle (we love ruins!); etc. We also happened on a historical re-enactment (the execution of Charles I) in downtown London the last Sunday of January – 14-foot pikes aren't something you see every day!
Oh, the Civil Engineers building at One Great George Street has a museum in its first floor library that is fun, as well as being a stunning building in its own right. (The library is a gem and oh-so-British!) When we went they had the world's longest suspension bridge built out of Legos; apparently their current year-long exhibit is of invisible superheroes. Very central location (right near Westminster and St James's Park). There is even a super-fancy café in the ICE building.
The Hunterian Museum near Lincoln's Inn Fields was fascinating – full of medical oddities – but is currently closed for renovation.
