You've got lots of good advice so just a few comments.

So glad to see Dennis Severs' House on your list. Was there in May, loved it.

Re a hostel in Bath, the one on Bathwick Hill is the better of the 2 HI hostels. Visited the one right in town then stayed at this one: http://www.hihostels.com/dba/hostel018010.en.htm

Everyone is right about Blenheim, pretty awful and I'm a huge fan of English Houses & gardens.

Try visiting Westminster Abbey for an afternoon evensong service. You won't be sorry.

My favorite museum in London is the National Portrait Gallery. A wonderful place. Around the corner from the National Gallery.

I think you'd do well to have an overnight in Oxford, probably instead of Cambridge. Each has it's partisans, I like Oxford better and a bit easier to get to from London. Walk a bit on the Thames path or along the Oxford Canal.

I'd also suggest a walk around Hampstead, lots to see: Kenwood House, Keats House, Fenton House, 2 Willow Road - these are the places I've been but there are more plus the village and the Heath.

I've also stayed at the YHA hostel joannay recommends. The building is lovely, but the bed was pretty hard. If you're just there for a night, that might not be a problem for you.

Do check into the YHA hostels in London - www.yha.org.uk - for reasonably priced accomodation. Some of them include breakfast in the price, but I've noticed most of them don't have self-catering kitchens anymore.

Lee Ann

I don't think LSE has been mentioned - London School of Economics, they rent out student accommodations in certain periods. A fair bit of choice for location and some have kitchens and private bathroom, costs vary of course.
http://www.lsevacations.co.uk/

It says singles from 27 pounds per night - super cheap for London.

Kay