A health minister has said “details are emerging” of Boris Johnson’s social care reforms, amid reports the Prime Minister is backing a new tax.

Lord Bethell hinted that progress is being made on the long-awaited proposals, with the aim for an “affordable, high quality and sustainable” adult social care system that meets all people’s needs.

Downing Street also did not deny reports that Mr Johnson is backing a new tax to pay for social care reforms or that a cap on payments could form part of his plans.

Both The Times and The Daily Telegraph reported a deal is imminent.

Mr Johnson is under increasing pressure to offer details on the plan, which he said was ready on the steps of Downing Street in 2019.

Lord Bethell’s remarks came as peers considered calls for a state-owned company to provide insurance for homeowners against having to sell their properties to pay for elderly social care.

Speaking in the debate, Lord Bethell said: “Can I say to Baroness Watkins of Tavistock that the Prime Minister has been very clear that we need a long-term plan for social care and, as she will know from today’s papers, the details are emerging as we speak.”

A No 10 spokesman said: “I’m not going to start commenting on speculation. No decisions have been made and we will set out the details later this year.”

Conservative former social security secretary Lord Lilley voiced concerns over the reported proposals and its impact on red wall voters.

Moving his Elderly Social Care (Insurance) Bill, Lord Lilley said: “At the last election, Labour promised to set a cap of £100,000 on the maximum cost anyone would incur while in residential care for social care.

The owner of a modest partly mortgaged home in Middlesbrough will see its value disappear entirely in two or three years. That's not a good proposal to go down well with the red wall voters

“And today we read in the Daily Telegraph that the Government could as early next week adopt that policy, hoping no doubt for bipartisan support.

“But it’s not Labour’s support they need but that of homeowners and the general public.

“The problem is that a £100,000 cap would be fine for the owner and heirs of a £10 million mansion in Mayfair even if they spent decades needing substantial care for dementia.

“But the owner of a modest partly mortgaged home in Middlesbrough will see its value disappear entirely in two or three years.

“That’s not a good proposal to go down well with the red wall voters.”

Lord Lilley said raising the value of assets shielded from means-testing will still mean many homeowners having to “sell their homes to pay for longer periods in care”.

He went on: “Both those options break the Prime Minister’s promise, repeated in his first speech as Prime Minister, to protect you or your parents or grandparents from the fear of having to sell your home to pay for the cost of care.”

Lord Lilley also said both options are “expensive”.

I cannot promise the Government will support the Bill. I can assure him we have carefully considered its points and its insight has provoked a timely dialogue

Instead, his Bill calls for people of state pension age to agree to pay an insurance premium of £16,000 to a state-backed guarantor.

The state would then cover the costs if a stay in a care home was required in later life, with the fee taken from the sale of a property after death.

Conservative Lord Cormack said social care reform is an “urgent crisis” and backed Lord Lilley’s ideas, before adding: “We’ve got to face up to the fact that we cannot afford the National Health Service unless we have a special tax or charges on certain things from able-bodied working people, often earning high salaries, or a combination of the two.”

Responding for the Government, Lord Bethell said the Bill addresses the “pressing issue of unpredictable and catastrophic” adult social care costs.

He added: “I cannot promise the Government will support the Bill. I can assure him we have carefully considered its points and its insight has provoked a timely dialogue.”

After he highlighted the lack of private insurance products, Lord Bethell also noted: “The Bill does shine a valuable light on a classic but nonetheless long-standing and damaging market failure, and it therefore it provides a strong case for Government intervention.”