I used to spend a lot of time reading in parks when the weather was decent. My favorite was a tiny park in Mayfair that was great for people watching. There are tons of museums to visit if that interests you. I loved all of the interesting London Walks. Pick up a brochure or visit their website:
http://www.walks.com/
I enjoyed the Jack the Ripper walk but the Royal Wedding and Harry Potter walks look like fun too. I lived in London many years ago but I miss it a lot (not the prices though!) Have a great trip!