The leader of Surrey County Council has been secretly recorded telling colleagues he had secured a "gentleman's agreement" with ministers on social care.
David Hodge is heard telling them he had spoken directly to the local government secretary, who intervened with the Chancellor, before calling off a damaging referendum to raise council tax.
Mr Hodge and Downing Street last month both denied there was a "sweetheart" deal to get more social care funding for Surrey after it was raised with Theresa May at Prime Minister's Questions.
But in a leaked recording obtained by Sky News, Mr Hodge explains he has called off his demand for a 15% rise. The council opted for a 4.99% hike instead, which does not require a referendum.
"There may come a time, if what I call gentleman's agreements the Conservative Party often does, are not honoured, we will have to revisit this in nine months or a year's time," he says.
"If we do, let me assure you that you'll have to drag me kicking and screaming not to go for a referendum next year."
Mr Hodge continues: "A series of conversations took place with the secretary of state for local government in his car outside Number 10 Downing Street looking for assurances, looking for clarification, looking for help basically for how we can stop the referendum.
"He then went inside and spoke to the Chancellor and his adviser … then the spad (special adviser) rang me with what we can and cannot say. There are certain things we cannot say, and yes there are certain risks to the decision we decided to go with."
He adds: "But every one of us knows in this room that we have what we call a gentleman's agreement with the Chancellor and the secretary of state."
Mr Hodge warns colleagues not to discuss the arrangement publicly.
Gareth Thomas, Labour's spokesman for local government finance, said: "Theresa May and her ministers, including Sajid Javid, have been playing political games, conducting backroom sweetheart deals for their friends, whilst councils across the country struggle to cobble together the money to adequately fund social care.
"Theresa May must come clean about the terms of the deal offered to Surrey County Council, apologise for her Government's misleading suggestion that there had been no such deal and ensure other local councils get the same treatment."
Lib Dem leader Tim Farron said: "This was denied by both sides. The PM called this 'alternative facts'. She should now come to the House of Commons and apologise."
Mr Hodge told Sky News it was "deceitful" of a colleague to record the private meeting and make it public.
But he said: "There's nothing I can do about it. I'm straight and honest. All I ever wanted is the best for the people of Surrey, I make no apology about that."
He said he had previously been asked by fellow councillors "to go and negotiate with the Government for the best deal we can get".
The meeting of the Conservative group on the council is understood to have been held in late January, on the day the council signed off its annual budget.
In the Commons, Jeremy Corbyn accused the Prime Minister of giving Surrey a special deal, while other councils across the country were left struggling.
In a statement, Mr Javid's department said Surrey was taking part in a pilot scheme to allow the council to fund social care from business rates from next year.
Mr Hodge insisted it was not a special deal for Surrey council, in which a number of cabinet ministers have constituencies, and that other councils may be granted the same arrangement in the Budget.
Social care is expected to get a funding boost of £1.3bn in the Budget, after a number of Conservative MPs and councillors expressed concerns that the sector was in crisis financially.