Take the tube to the end of the line at Richmond, then hop on a bus and you'll be dropped off outside of Petersham. This was my second trip. I remember years ago, it was very delightful. It still has the same delightful charm. This was the flowers at the main restaurant which require a reservation but they have a little cafe which sells salads, cakes, tea and coffee which does not require a reservation. This trip in June 2016 I took the bus to Ham house which was a mile further, then I walked the Thames path to Petersham. It was the loveliest day. England in June is glorious. There's only one June every year. Don't waste it. I intend to be out and about in England every June.