Labour has made no contact with other parties over new talks to resolve England’s social care crisis, amid fresh demands for a workable plan that secures cross-party support.

Wes Streeting, the health secretary, said over the summer that he was keen to hear ideas from across the political divide as part of a renewed attempt to make progress on a crisis that has remained unresolved for more than a decade.

However, Tory and Liberal Democrat sources said they had received no approach from the government over a new programme of talks. There have also been suggestions that the government will set up a royal commission to find a solution, though industry figures said they had not heard that such a move was coming.

A Whitehall source said the government was working on its plans for social care and that it was too early to be discussing cross-party talks, given that the government had only been in office for two months.

Since the election chancellor Rachel Reeves has scrapped a cap on social care costs due to come into force next year as part of her cost-cutting drive. The measure was expected to cost £1bn a year. Nothing has yet been announced in its place. The care industry is warning the sector is suffering with underpaid staff and unfilled positions, while cash-strapped councils are struggling to cope with a swath of people unable to afford their care.

In reality, some senior figures in the Labour government do not see cross-party talks as the answer to unlocking the social care problem. They pointed out that previous talks were effectively meaningless, because those involved refused to agree on the funding of the plans. “In the end, this is a political decision,” said a senior official.

Streeting made the case for cross-party talks to improve the current system before the general election. “The Lib Dems have got some good ideas, other parties have got good ideas, let’s try to work together … to see if we can do something that has escaped and eluded every single government,” he said.

Insiders reiterated that since entering office, ministers had found a health service in a worse condition that they had feared. However, they said they needed to carry out a thorough review before imposing any reforms on social care.

It comes amid concerns in Whitehall about the degree to which the government has ruled out personal tax rises, given the strain on health spending. Extra pressure has been exerted by Labour leader Keir Starmer’s subsequent pledge not to inject more money into the health system before NHS reform has taken place. Senior figures are understood to be urging him to make it clear that reform should happen alongside upfront funding. They argue that the government cannot afford to delay boosting the NHS’s finances.

The Lib Dems have put improving care services at the heart of their pitch to voters. “It’s clearer than ever that we can’t fix the NHS unless we fix the crisis in social care,” said Helen Morgan, the party’s health and social care spokesperson. “Thousands of elderly patients are stranded in hospital beds, piling pressure on local health services and leaving people without the dignified care they deserve.

“We know that this crisis will only get worse with an ageing population, so there is no time to waste. We stand ready to work with the government to resolve this issue, through cross-party talks on social care to find a long-term solution. We are really worried that care and carers have been forgotten by ministers for far too long, and we’re determined to make sure that doesn’t happen now.”

Shadow care minister John Whittingdale said: “This new health secretary had promised a lot, but so far we’ve seen very little. His pledge to work cross party to tackle the challenges facing our social care sector was the right thing to do, but until he follows through his words are empty.”

The Department of Health and Social Care said: “Our social care system is broken, and it is unacceptable that so many people are being left without the care they need. We are committed to building a national care service, underpinned by national standards and delivered locally, to ensure everyone can get the care they need. We will build consensus on long-term reform, and engage with a range of stakeholders, including cross-party and those with lived experience.”