Reforming the social care system in England is “urgent”, cabinet minister Louise Haigh has said, after sources told the BBC there was a “genuine impasse” at the top of government over the issue.

The transport secretary said the government had already taken steps to improve pay and tackle vacancies in the sector, as well as giving councils an extra £600m in funding for adult and children’s social care.

In its election manifesto, Labour promised to create a National Care Service to deliver consistent care across the country – but so far the party has given little detail on what this would look like.

Liberal Democrat leader Sir Ed Davey called for cross-party talks on how to reform the system in the long-term, but said there also needed to be “immediate measures”.

The prime minister, health secretary and chancellor are due to meet in the next 10 days to discuss the issue.

Multiple sources have told the BBC the Department of Health is keen to proceed with an overhaul of the social care system but that the Treasury is reluctant to commit to significant costs without clear political backing from Number 10.

“It’s really urgent that we fix this issue,” Haigh said.

“For too long we’ve let this problem fester.”

Pressed over whether the government was taking the problem seriously, she told the BBC’s Sunday with Laura Kuenssberg programme that the health secretary had already set out a 10-year plan for the NHS which included focusing on prevention and community care, which she said would “ease pressures on social care”.

She also pointed to the government’s plans to improve pay and conditions in the sector through a Fair Pay Agreement, allowing negotiations between workers, unions and employers.

“We need to make sure we are tackling those long-term issues in the workforce, with progression opportunities, properly paid and properly negotiated on a collective basis,” she added.

Ministers are considering whether to create a Royal Commission, with cross-party involvement, to consider how to reform the social care system, or a shorter government-backed independent review.

Sir Ed said although the Lib Dems would back a Royal Commission there needed to be “immediate measures first” and it “must not be an excuse for long-grassing this”.

He said there were things the government could do “straight away”, for example on tackling vacancies in the sector.

The Lib Dem leader called on the government to be “more ambitious”, pointing to his party’s own proposals for a higher minimum wage for care workers.

“Politicians have been failing on this for far too long,” he told the BBC.

“There are millions of people suffering, families being hit financially, people in misery and pain, and we have got to tackle this.”

He added that the Lib Dems were “willing and ready” to take part in negotiations over the issue but he had not yet had a call from Health Secretary Wes Streeting to do so.