Your children are older than mine is, but we just got back from a trip to England and Scotland where we visited London, Oxford, York, and Edinburgh. Below is what we did with our kiddo (5.5 years old at the time of the trip) that were notable:
London:
- Tower of London: be sure to do the (free) Beefeater tour. Typically pretty crowded, but the guides do a good job of engaging the children. We arrived right at opening and went straight to the Crown Jewels. It wasn't crowded at all, so we got to take multiple "rides" on the moving walkway and our son thought that was really cool.
- My hubs and I have done the Churchill War Rooms (pre-child) and although it was really interesting/informative, it is a LOT. Our kiddo would not have been engaged there at all. Yours are older, so maybe they will be. But I'd be prepared with backup activities if you plan to spend more than a few hours there :)
- Princess Diana Memorial Playground in Kensington: large playground, great for all ages, worth going out of your way for. You can also enjoy Kensington/Hyde Park.
York:
- there's a Rick Steves walking tour in the guidebook that takes you through the ruins of the former Abbey there. Our son thought that was great and he liked running through the park.
- Jorvik Viking Center: we did this and thought it was ok. The ride portion was fairly interesting, but the displays (we felt) are poorly laid out and too cramped. We're not mad we did it, but we certainly won't do it again.
- Yorkshire Museum: I thought this was really interesting and had some good kid-friendly exhibits.
If you do stop in Oxford:
- the Ashmolean Museum family adventure. Our son LOVED this. It took us to some exhibits we wouldn't have visited otherwise. Really fun for the whole family. (https://www.ashmolean.org/families)
Edinburgh:
- Edinburgh Castle
- Day trip to Glasgow: we were shocked how much we liked Glasgow.
- Scotch Whisky Experience: not a distillery, but it was a good combination of stuff for the adults (whisky tasting, informative, good overview of Scotch whisky) and stuff to keep kiddos entertained (starts with a ride, has short movies and special effects). I did the silver and my husband did the gold tasting and we did not feel that the gold was worth the extra money, but we're also not big Scotch drinkers.
- Day trip to St. Andrews: if you will be in Edinburgh on a Sunday, I would say this is a DO NOT MISS. Even if you're not a golf person. On Sunday, you can walk the Old Course of St. Andrews and it is such a cool, unforgettable experience. We also really liked the town of St. Andrews. (Of course, we were there in late November, so summer crowds might make it less appealing?)
I hope this helps somewhat, have a great trip!