Since you intend going to Stonehenge (a good idea, IMO), I'd like to suggest a route out of London taking in Oxford, Bath and Salisbury too. I did that exact trip a few years ago finding accommodation as I went - I stayed in pub / tavern type places. It might be a little more expensive than more modern hotels, but a lot more memorable. I don't have details of places unfortunately, but it wasn't difficult when travelling by car. Have you thought about how you'll get around?
I remember weird details about that trip, like the cinema in Salisbury, check out this page and you'll have some idea why:
I didn't know about this place before visiting Salisbury, just wanted to see a film. I asked a local for directions to the cinema, they grinned at me and said it was rather a peculiar building and they'd better take me in person or I would think they were playing a trick on me. The film I saw was terrible, but I won't forget the cinema. Salisbury Cathedral was the reason I visited the town, that was also a remarkable place (I'm biased, having studied medieval history and having done a stone masonry internship at Canterbury Cathedral - this might not be your thing).
The Victoria and Albert Museum is great, I always visit when I can.