The Association of London Government has postponed a decision on the future funding of Carers London until September.
Following protests from carers' centres and projects, the grant maker, which represents London's 33 councils, has backtracked on an earlier decision to end the charity's £140,000-a-year funding.
But the London-wide carers' organisation, which was set up by national charity Carers UK, is still warning that if the grant is not reinstated, it will be forced to close as early as October.
Carers UK chief executive Diana Whitworth said: "The reprieve is temporary but it offers carers in London a chink of light.
"Our funding is due to run out in October, which leaves us very little time to find funding elsewhere - the Association of London Government is our only realistic hope of saving the service."
At a meeting last week, the association also voted to defer a decision on future funding to Deaf Plus, the Occupational and Environmental Disease Association and the Westminster Pastoral Foundation.
This year's bidding round, which covers areas such as children and young people, health and social care and citizenship and human rights, was heavily oversubscribed with 600 applications in excess of £47 million for a grant pot of just £8.3 million.
The Association of London Government had instituted the first major review of its grants since 1985, drawing up new criteria for groups to apply for funding.
But according to Carers London, if its grant is not approved in September, this would mean that the association was failing to meet a stated priority of funding carers on a pan-London basis.
But Mark Freeman, chief executive of sector consultancy Charity Business, said that Carers London should have looked to diversify its income. "This scenario demonstrates a serious lack of financial strategy, but it's certainly not unique. Too many organisations are dependent on grants and other forms of single-source funding."