In London I took the sight-seeing double decker bus trip the evening of my arrival. Tired due to travelling, long day, etc. so the bus was a great way to see the lay of the city and note places I wanted to come back to for further exploration. The walk through Green Park on the way to Buckingham was pretty cool. As a major plant weenie it was great to see some ginormous trees as well different ways the Brits handled maintenance of their green spaces. My trip was almost the same time (late May) last year. I missed the Chelsea show by 1 day, but had great chats with some garden-installers who were staying in my hotel (even if we understood about 1/3rd of what we were trying to say to each other!). See what events may be going on like a Chelsea or a special event at Kew. Have fun!