Anyone coming to London should put Kew Gardens on their to-do list during their visit.  I'm not a "garden" or "flower" person by any stretch, but spending an afternoon out there last Fall started to change my mind on the topic.  Kew is a massive garden complex out near Richmond, about 40min outside of London, and is loaded with greenhouses and gardens of all types from arid desert fauna to more tropical specimens.  They've got a full Japanese garden and pavillion, complete with pagoda, a section with interesting stunted redwoods, that grow much shorter than they do in California apparently (less light and inferior soil!), and they have quite the collection of water lillies, some of which can be seen here, to name just a few highlights.  It’s a pretty impressive setup even for us non-experts, and a very enjoyable way to spend a summer day, highly recommended.