Knowing your love of flowers, even though it is the wrong time of year for outside stuff really, you could call into Kew gardens, which is not that far from Hampton court. They have loads of stuff under glass. Also Sion Park, in the same sort of area has a nice old house, and a butterfly house under glass. Hope it dries out for you a bit before you land, we are a bit wet and muddy down this end of GB at present. Wave as you fly over, we are on the flight path into Heathrow airport about 20 mins drive away.

The greatest part of wisdom is learning to develop  the ineffable genius of extracting the "neither here nor there" out of any situation...."