Theresa May admitted that the government did strike a deal with Conservative-led Surrey County Council at prime minister's questions (PMQs) on Wednesday (8 March).
But the Tory leader stressed that the agreement was open to other local authorities, including councils in Liverpool, Manchester and London.
"The substance of what he's asking is has there been a particular deal with Surrey County Council that is not available to other councils? The answer to that is no," May said in response to Jeremy Corbyn's question.
The Labour leader asked: "Could the prime minister explain the difference between a sweetheart deal and a gentleman's agreement?"
The exchange comes just a day after a recording of Surrey Council leader David Hodge was leaked. Hodge told his Conservative colleagues that a "gentleman's agreement" had been made with cabinet ministers in a bid to scrap a 15% hike in council tax to pay for social care.
However, instead of using all six questions to press May on the issue, Corbyn switched to the issue of schools in England and Wales. The Chancellor Philip Hammond failed to deny reports over the weekend that he would unveil £1bn in his spring Budget for social care.
"We recognise that there are pressures in the social care system and that those pressures are having an effect on the way the NHS works but it isn't just about money," he told ITV's Peston on Sunday show.
Labour's shadow City minister Jonathan Reynolds told IBTimes UK that May could face a mutiny if Hammond does not address the "crisis".
"We think Hammond must move to tackle the crisis in health and social care funding – he'll face a mutiny on his own side if he doesn't even acknowledge how difficult the social care situation is – and address the squeeze on living stands caused by the chronic level of low pay combined with rising inflation," he said.