London Councils has called on the government to provide at least a 9% funding boost in the Autumn Statement to help meet a £600m shortfall.
The body, which represents the city's 32 borough councils, forecasts the collective annual overspend has increased by 50% due to a spike in spending between June and September.
This is due to "London's worsening homelessness crisis", it said.
The chancellor is due to set out his spending plans on Wednesday.
As well as the 9% funding increase, which would be in line with last year's Autumn Statement, the cross-party body has also requested that the government invest in homelessness initiatives and "reforms to the broken local government finance system", a spokesperson said.
Councillor Claire Holland, acting chair of London Councils, said the current demand on homelessness services was "utterly unsustainable".
"Alongside massive demands on adult and children's social care services, spiralling inflation, and insufficient funding from government, boroughs are left in an extremely precarious position," she said.
'Weather the storm'
About one in 50 Londoners are currently homeless, according to analysis from the group.
Homelessness services in the capital are facing a £150m overspend, it said.
Ms Holland called on the chancellor to help London's local authorities to "weather the storm".
Enfield Council said there was "no evidence" it would go bust, despite £1.12bn of debt, the 10th highest of England's local authorities.
London Councils said despite there being 800,000 more Londoners since 2010, London boroughs' resources remained a fifth lower than they were 13 years ago.
A government spokesperson said: "London Boroughs have seen an increase in Core Spending Power of up to £744m (9.3%) on 2022-23 - making available a total of up to £8.757bn in 2023-24.
"We are determined to prevent homelessness before it occurs and are providing London councils with £350m funding through the Homelessness Prevention Grant to help those at risk access the private rented sector."