Library Gardens is the level park behind the Churchill Theatre; you then go down the slope to the integrated Church House Gardens. Originally they were the gardens to Neelgharies House. Part of this site, including the public conveniences (which the council has allowed to become derelict) will be sold to the Site G development. It looks like the Deodore Cedar tree will be saved. See more about it at the Friends page here.
Traditionally this area was formal gardens with a flower clock, the hands of which were set to the Library closing time.
Church House gardens still retain a formal area, and originally included the fish ponds, on which was built an amphitheatre and performance structure, now derelict. Please see the full description on the Friend’s site, here. Part of this park, Dickerson’s Copse., might be chopped down for the Site G proposals.