The Chelsea Physic Gardens say they have a microclimate that supports more tropical plants. I enjoyed the other half of the garden more, where they explain where medicinal plants come from and what they're used for. There's a riverboat pier near there too.
RHS Wisley is also fantastic. Unfortunately slightly more difficult to get to; you really need to drive there.
Agreed about the riverboats. Tried the Thames clippers for the first time a few weeks ago. They're delightfully empty during weekdays and serve drinks and snacks on board.
My next stop has to be Kew Gardens!