Marble Hill is a heritage house and park near East Twickenham in the London Borough of Richmond. The park extends down to the Thames. There is a manmade grotto in the park.
I walked upstream along the Thames from Richmond bridge, and entered the park from the river path.
See more on the Historic England site, where there is a drawing of the grotto surrounded by shrubs, as well as a lot of information on the house and grounds. This blog has more info and some good photos of the grotto surrounded by shrubs (2012). I don't know if there are plans to restore the shrubs or why they were removed in the first place.
And English Heritage places to see.
"June 2021, two subterranean grottos in Twickenham will be having synchronised open days on the same day. Grottos were the height of fashion in the early eighteenth century and Twickenham is home to two of the most spectacular examples. The Pope’s Grotto Preservation Trust and English Heritage, supported by the National Lottery Heritage Fund, are offering a rare chance to visit both Alexander Pope’s grotto in Cross Deep and Henrietta Howard’s grotto at Marble Hill in one day."
However when I tried to book one month before, tickets were already sold out.
UPDATE FEB 2022
At the end of Feb 2022 I went back to Marble Hill to see if the grotto was open, but found an archaeological dig was in progress. The notice board says they are removing the soil to reveal Henrietta Howard’s lost grotto.
I don't think it will be open by the spring as the notice suggests!
This English Heritage page gives more info on the updates to the grotto work, Nov 2021 and some of the finds.