However, it also warned that volunteers could not be expected to take on the roles of professionally-trained staff.
The trust is the latest incarnation of the Land Restoration Trust, a former subsidiary of the Homes & Communities Agency now operating as a charity and including the National Trust, British Trust for Conservation Volunteers and Town & Country Planning Association as members.
It published figures showing that in the three months since becoming an independent charity, its 18 active spaces have "delivered bumper community outputs".
From April to June this year, its sites attracted 2,000 people to improve their health, 1,000 school children attending educational sessions, 100 people attending practical training events and 239 days of volunteering activity.
In a statement released with the figures, the trust said the "impressive" number of volunteering days demonstrated "that the thinking behind the Big Society - that people want to play an active role in their communities - is sound".
Chief executive Euan Hall said: "The trust considers 'localism' and the Big Society to be key to our collective future. We believe that people should have a real say in shaping the places where they live. The fact that we have encouraged so many people to get involved in managing open spaces shows it can work.
"It's also important to note that these spaces aren't in leafy suburbs or affluent middle-class areas. In the main, they are communities considered to be deprived."
However, Hall did offer a note of caution, arguing that volunteers must be supported. "It's not right to expect volunteers to do in their spare time and for free what full-time, highly-trained people get paid for," he said.
"Even the most basic open spaces need public liability insurance, financial controls, land management plans, fundraising schemes, marketing and biodiversity planning as well as the physical maintenance of the site.
"Without a secure umbrella organisation like ours giving advice and support, the work is left to a few hardy souls who gradually become more and more disenchanted. Localism can definitely work but the community has to be supported - not just for a few months or even years, but long term. That way we are not creating the regeneration areas of the future but a true Big Society."
Parks consultant Stewart Harding criticised the proclamation. "The Land Trust is merely jumping on the Big Society bandwagon," he argued.
"Volunteers have been an important aspect of the running of parks and open spaces for decades - long before Cameron coined the Big Society phrase and long after Margaret Thatcher declared in 1987 that there was 'no such thing as society'. I agree that volunteers need a secure umbrella organisation, but our democratically elected local authorities have been providing this for decades.
"It is nothing to do with the Big Society idea - it's just society working normally - and to do this funds are required, such as the recently frozen Playbuilder programme, or indeed the Land Trust's resources."
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