Hi Francis,
Back in May-June we visited a number of gardens. In no particular order, our faves were:
Hidcote and its neighbour Kiftsgate. We luckily had the latter to ourselves after a brief summer shower chased a busload away. That resulted in no other visitors for the two hours til closing. Some folks had warned us that Hidcote was too commercial and touristy, but we experienced nothing but wonder there, with cheerful friendly staff and a wide variety of quality attractions.
Kew was excellent too. We'd bought memberships in order to get in early at 8 am (also included free mailings of their superb magazine). That meant far fewer visitors til the regular 10 am opening. It was an annual school visit day, with dozens of school groups of every age. we met one class of 6 yr olds from Battersea PS. We were told by their chaperone that those kids' grandparents had once been the young voices heard singing the famed chorus ("WE DON'T NEED NO EDUCATION!") on the Pink Floyd hit 'Another Brick in the Wall'. We also chatted with a gardener gal there who was mere hours away from her retirement from working at Kew.
Another pair that impressed were the Isabella plantation at Richmond park, plus the Golders Hill garden next to Hampstead Heath. The latter has a wonderful pergola, plus proximity to the actual village of Hampstead. The former is well worth the hike, which takes one through the remote woodland of Richmond Park proper (*making news just now given its having turned unusually dry due to lack of water).
If in Chipping Campden, there exists a pair of lesser-known, B-league gardens that nonetheless make for brief interesting tours. One is the tiny Ernest Wilson memorial garden at the top end near the main church. Some very rare items there. Also, the back gardens of the luxe hotel 'Cotswold House' are among the finest such quasi-private ones that we've ever visited. Small but wonderfully designed and maintained.
We will soon display our photos of all the above in our upcoming Trip Report, both here and also over on the Fodors forum.
I am done. The end.