Just to throw another 2p into the discussion. I will admit, I no longer live in the UK, but I am a native Londoner. While I would agree the North of the UK (Scotland) is a wonderful place to visit, I would agree with the suggestion from Jon_1066 and say you're better off staying in the south (Unless you massively extend your UK part of the trip). If you are able to hire a car from Heathrow airport there are a large number of very nice places to see between London and Bristol.
I can suggest finding a hub location somewhere in/near Marlborough (a very pretty and historic town). That would then put you within ~1hr of Oxford (including Blenheim Palace), Bristol, Winchester (a LOT of history), Salisbury, Bath, Andover (Army Flying Museum), Stonehenge, and Windsor (Highly highly recommend the castle there) etc. You would also be within about ~2hrs of a large stretch of the south coast if your family would like a day at the seaside.
If you do go into London, I can highly recommend the Tower of London, as a place to go and visit. Get a on Yeomen warder tour. They are brilliant and the Yeomen do a great job of bringing the history to life. The Museums are good, but can be quite dry. And the theater scene has been hit hard so difficult to predict what will be running. On a side note, if you do stay in London, I can recommend not trying to save on the hotel. There are a lot of very poor hotels in London that are still reasonably high prices, but budget for London. If you pick on, you will likely regret it and it would be a shame to have that as it can ruin a trip. Sadly it is worth getting a nicer hotel for your stay. But that is pretty much a London only problem!