Natasha Fuller, whose children use the playground, said it was “such a shame it has got to this point” after “nearly 50 years”.
“The amount of things they come here and do, there’s such a good set up here,” she said.
“One of the biggest reasons I’ve stayed [in Blackbird Leys] is because of BLAP.”
Tansiha Macklin-Carr, play and project manager at BLAP, said the charity was “a really good support system” for children in Blackbird Leys.
“We have got a great bunch of kids and a great bunch of parents – it’s one big BLAP family,” she said.
The charity currently has three members of staff, and is looking for new volunteers, as well as a treasurer and accountant.
But volunteer Kirsty-Ann Mabbott, said the charity was struggling to fill the positions because of “where we are”.
“People cannot afford to be volunteering when they need to be working and earning money,” she added.
Greater Leys is one of several areas across the UK that will get a £20m cash injection over ten years from the government as part of its Pride of Place programme.
Local councillor Hosnieh Djafari-Marbini, who used to be a trustee at the charity, said boards to decide how to spend the money would not take place until next year.