Kensington and Chelsea Council says it stands to lose £108 million over four years if the proposals go ahead.
A public consultation found 93% of nearly 1,500 respondents backed its plans to challenge the changes.
The councils have confirmed they are preparing formal proposals asking ministers to reconsider how authorities are funded.
Councillor Elizabeth Campbell, Leader of Kensington and Chelsea Council, said:
“The Government calls this fair funding, but taking £108 million from our borough – more than 40 per cent of our controllable budget – is the furthest thing from fair. This is unfair funding, plain and simple, and an unprecedented reduction that will mean incredibly tough decisions and stark consequences for our residents.
“I have been clear from the beginning that I will exhaust every avenue to challenge this decision. As Leader, I could not stand in the Council Chamber and announce decisions affecting residents’ lives knowing there was more we could have done to persuade the Government to think again.
“And this is not just our fight – almost 1,500 residents responded to our consultation, providing more than 300 pages of comments about what these cuts would mean for them. I will be sending their words directly to ministers so they understand that it is not just the Council saying this is wrong, but the people we represent.”
