...lived here. You may remember seeing her gravestone in St Andrew's Churchyard...

Her Wikipedia entry notes:

She bought the land opposite the house for the benefit of Clifton residents and it still remains green space

While there is some green space opposite, it looks very private and seems to belong to Edgecumbe Hall (sometimes spelled Edgecombe, it seems...)

CHIS's Communal Gardens web page says:

Richmond Hill Gardens. ca 1830 This forms a key visual feature at the top of the triangle. There are specimens of at least 23 tree species, including a magnificent Weeping Beech, the finest in the city, and a Redwood, which is an offshoot of a tree cut down twenty years ago. The land was bought by Sarah Guppy (1770-1857) an inventor and designer who was consulted by Brunel. She lived in Richmond Hill and did not want any building opposite, so bought the land and made it communal. For many years it was a nursery garden but now it has become a well hidden car park for those houses to which it is attached.

...and lists it under "Private Communal Gardens", so I suppose it's not public, but it is communally-owned (and likely to have a covenant against building?) Seems a bit of a shame it's ended up as a car-park.