The proposed cut, which was due to be debated by councillors on Tuesday evening, will also hit a number of other green space projects in the borough including the Centre for Wildlife Gardening, Surrey Docks Farm and Walworth Garden Farm.
In a letter to Bankside Open Spaces Trust supporters, director Helen Firminger said without the funding that supports the trust's core parks work and enables it to bring in further funds, it was unlikely the organisation could continue.
The total grant for the trust and the other green spaces projects is expected to fall from £311,536 for 2010-11 to £67,534 in 2012-13. The trust has improved and maintains numerous green spaces in north Southwark.
In its response to Southwark's consultation on the cuts, the trust said: "These projects are vital to local communities providing a life-affirming resource to focus active citizenship, volunteering, mental well-being and community action."