I’m starting to compile as many definitions of public space as I can from here.
First, the definition from the London Assembly’s 2011’s report, ‘Public life in private hands Managing London’s public space’, which started to acknowledge the massive shift to privately-owned public spaces in the capital.
‘all spaces including streets, squares and parks that everyone can use and access in principle, regardless of who owns or manages the space’.
The 2011 report also quoted the 2004 government report, Living Places: Caring for Quality, https://www.futurecommunities.net/files/images/ving_Places_Caring_for_Quality_Report__ODPM_.pdf, which defines ‘public realm’ as
‘all those parts of the built environment where the public has free access. It encompasses: all streets, squares and other rights of way, whether predominantly in residential, commercial or community/civic uses; the open spaces and parks; and the ‘public/private’ spaces where public access is unrestricted (at least during daylight hours). It includes the interfaces with key internal and private spaces to which the public normally has free access’.
The 2011 report notes ‘this is different from the legal definition in the Town and Country Planning Act of 1990’ (https://www.legislation.gov.uk/ukpga/1990/8/section/336)
“open space” means any land laid out as a public garden, or used for the purposes of public recreation, or land which is a disused burial ground’
and the more traditional planning definition of Public Open Space.
It also notes the additional category of ‘public green space’, including urban parks and gardens, country parks and canal and riverbanks.
See also the 2014 government guidance about the definitions of Open Green Space in replation to planning and sport: https://www.gov.uk/guidance/open-space-sports-and-recreation-facilities-public-rights-of-way-and-local-green-space