Havering Council could go bankrupt in as soon as six months, its leader has said.
Ray Morgon blamed supplier costs and spending on social care and housing for the problems.
He said central government funding had “not kept up” with inflation since it was frozen in 2013, and “is not fit for purpose”.
The Department for Levelling Up, Housing and Communities said it would speak to any council with financial concerns.
Havering Council, which has no single party in overall control but is led by Havering Residents Association, had previously warned “the situation is desperate”.
Mr Morgon said the authority’s new financial director estimated “in six to 12 months, yes we could be at the point where we have to issue a section 114 notice effectively saying that we’re bankrupt”.
He told BBC Radio London the cost of living was exacerbating issues for the council, adding: “Our contractors and suppliers of services, they’ve raised their prices quite dramatically.
“For example, we are placing a resident in a care home outside of the borough because she wanted to be closer to her family.
“Suddenly the provider said it’s no longer £800 a week, it’s £2,000 a week.”
Mr Morgon said the council would “look very carefully” at its costs but the authority was ranked by independent bodies to be one of the most efficient and cheap, so it would be “a challenge”.
“I don’t believe it’s necessarily going to bridge the gaps we’re talking about in terms of demand for both social care and housing services,” he added.
The council leader said parking charges could be among the costs that could increase, but “we certainly don’t want to be in the position Croydon is in… with a 15% increase in council tax this year”.
A Department for Levelling Up, Housing and Communities spokesperson said local authorities had seen an increase in core spending power of up to £5.1bn in 2022-23, with almost £60bn available for local government in England.
“For Havering Council, this represents an increase in core spending power of up to £18.5m (9.2%) – making available a total of up to £218.7m in 2023-24,” the spokesperson said.
“We stand ready to speak to any council that has concerns about its ability to manage its finances or faces pressures it has not planned for.”