As we are on a Disney site, I thought you might be interested in visiting Pooh Country. Unfortunately it is in the South where as it sounds you will be mostly in the North.
It is a village called Hartfield (near East Grinstead) which stretches into Ashdown Forrest, aka 100 Acre Wood. It is a beautiful walk through the forrest and you can get a map and find all the "enchanted places" that A A Milne wrote about and where the real Christopher Robin (his son) played as a child. You can see the house where Pooh was written, play Pooh sticks on the actual bridge, in fact it's kind of like looking at the map that you see at the start of the classic Disney film. There is a 3 century old shop which Christopher Robin used to visit with his nanny, that has now become a shop dedicated to the stories, called Pooh Corner. Apparently, it has the largest selection of 'Pooh-phernalia' anywhere in the world, partly Disney and partly the original Pooh (my favourite).
If time is short for you though, I would spend it mostly in London, there is SO much to do and see. I love visiting cities all round the world, with New York being my personal favourite, however I still think London beats all the others for tourist attractions. I live an hour from it and regularly do the tourist thing, but I don't think I could ever see it all. My top four not to miss
1: Tower of London
2: Leicester Square/Picadilly Circus/Oxford Street/Trafalgar Square (all close)
3: The museums (Natural History, Science museum, British Museum)
4: The London Eye
I have done the open double decker bus tours quite a few times with visitors, and I really think this is a good way of getting a overview of everything that is worth seeing in a short space of time. You can hop on and off and is well worth the money. I do these kind of tours when I visit cities abroad and I really feel I get a good overall picture of the city, it also helps me to decide where I want to go back to later on in the trip.
Have a great trip.