I took my daughter to England last July for two weeks and this is what she (7 yrs old) enjoyed.
Edinburgh: Edinburgh Castle - started our day below in the Princes Street gardens at the west end where there is a really fun playground. We then walked all the way up this winding path that ran along the base of the castle to the entrance itself. My daughter loved seeing the Crown Jewels of Scotland. We spent about three hours at the castle including a kid friendly lunch (mac & cheese). We then walked all the way down the Royal Mile to the Palace of Holyrood House which was open because the Queen was away. This palace has some really interesting features including the tower where Mary Queen of Scots lived. My daughter loved seeing her little bed! Following this we found ice cream and called it a day. We only spent one full day in Edinburgh but there is so much else to see.
We really enjoyed a day trip to Bath including the Roman Baths (about 90 minutes)& a City Bus Tour (hop on hop off). We discovered a great playground on the bus route (good for an hour while I sat in the sun).
Day trip to Hampton Court Palace was fun. Beautiful gardens, great rooms (the ceilings are breathtaking) and a fun maze.
Our time in London was amazing. Riding on the top deck of the red double deckers was great fun. The British Museum was actually quite interesting for her. So was the National Gallery (about 90 minutes each). The Museum of Natural History was great (2 hours plus we returned) but the Science Museum less so (we have a Science Centre at home). We also walked and walked but were never tired.
We skipped the Tower of London (too scary) but took the elevators up to the top of Tower Bridge and walked across. Skipped the Eye (too slow).
Enjoyed the playgrounds in the great parks. Diana Memorial Garden was great for an hour.
Kept energy levels up with icecream, biscuits, fresh fruit and deli items from Sainsbury's and Tesco's.