Here are some kid-friendly places:
1. In the Cotswolds area (consider renting a cottage for 3-4 days and explore the area)
Bourton-on-the-Water is a beautiful village, with a model village that's amazingly accurate and cute
Stanton: Cotswolds Riding Centre: kids can go on 30min-90min pony rides in the country side and into the village
Near Stratford-upon-Avon: Anne Hathaway's village has a beautiful garden, Mary Arden's Farm is an open air folk museum, with the staff dressed in Tudor costume, animal farm (my kids loved petting the rabbits and the shetland ponies). Lots of swans on the River Avon.
Avebury stone Circle: not as famous as Stonehenge, but you can walk amongst the gigantic stones, and pet the sheep grazing in the area
Hiking can be done almost anywhere. Beautiful countryside scenery. Always a treat to run into a flock of sheep.
North of Cotswolds you can drive to Iron Gorge, lots of museums. Enginuity is a very hands-on science/engineering museum, Blist Victorian town is a recreated Victorian Town.
Then you can head up to:
2. Lake District
Beatrix Potter farm, boating on the lake, Castlerigg (another stone circle), beautiful scenery, especially if the weather cooperates.
3 North Wales
Fun to see Welsh sign everywhere, lots of very well preserved castles built by Edward I when the English first took over Wales - Conwy, Caernarfon, Beaumaris, Harlech. Kids always love castles, and these have great signs geared toward kids.
4. York
Jorvik Center (Viking museum that features a Disneyland style ride thru a Viking Village), York Castle Museums has a recreated Victorian street and lots of informative displays.
5 London and nearby
Harry Potter Studio Tour in Leavesden
Legoland near Windsor Castle
Hampton Court- Henry VIII's old palace, kids will have fun looking at the old kitchen with giant fire place
in London: Natural History Museum (Simply amazing!Kids will love it.), Tower of London (look at Henry VIII's armor and mediaval potties!)
Coventry Garden: they will like the street performers and snacks.
London Eye
British Museum.
BTW, all the top museums in London are free, and kids ride on the subway/bus for free, too.