Havering Council anticipates being taken to court over its inability to keep up with rising homelessness.
A council report said the government was set to cut funding for homelessness services amid the cost-of-living crisis.
Homeless applications are already 59 per cent up on three years ago and are expected to keep climbing.
Paul McGeary, Labour cabinet member for housing, said officers were “working hard to try and cope with demand, but we really need support from central government”.
However, Darren Alexander, assistant director for housing demand, warned in a report that Havering’s Homeless Prevention Grant is “likely to be reduced by between eight and 26 per cent”.
“Families facing eviction and requiring emergency accommodation are likely to be placed in hotels for longer than the statutory six-week time frame,” he wrote.
“This presents a risk, both legally and financially. Challenges from local solicitors judicially reviewing the local authority’s ability to meet need and to provide temporary accommodation is also likely to rise.”
Pressure on the service is already forcing Havering to tell residents facing eviction from private rentals that it cannot help them until the bailiffs arrive.
“The service is fighting to effectively address homelessness by supporting households to remain in their accommodation as long as possible right up until bailiff warrants are issued,” said the report.
“We understand that this causes particular distress to families; the alternatives, however, do not make good reading.”
The report warned that evictions from private rentals were likely to increase.
The market is already “drying up”, wrote Mr Alexander, and more landlords are “expected to sell their properties” due to rising costs.
Between April and August 2019, Havering received 873 requests for help with homelessness.
It fell to 814 between April and August 2020. But in the same five-month period in 2021 it shot up to 1,339 and this year it rose again to 1,391.
“It could well get to a position where we aren’t able to cope with the tsunami of requests,” said Cllr McGeary.
The Department for Levelling Up, Housing and Communities did not respond to a request for comment about Havering's claim that it faced cuts to its homelessness grant.
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