The Conservatives’ manifesto pledge that no one will have to sell their home to pay for social care is emerging as a stumbling block over reform plans between Number 10 and the Treasury.

A gulf has emerged over whether housing wealth should be included in an assessment of eligibility for means-tested care and the level of a cap on the sums any individual has to pay privately before the state steps in.

With initial annual costs of a full package of social care estimated by the Treasury at £7bn-£10bn, ministers are split on whether to seek to cut costs, with families probably still needing to sell properties to pay for social care, or to fund a much larger state service.

Boris Johnson and Rishi Sunak met to discuss social care at the end of April. One person familiar with the discussions described the arguments as “very live”, but without agreement on a plan.

Next week’s Queen’s Speech is expected to see a fresh commitment from the government on reforming social care funding although without much detail, again falling short of Johnson’s pledge to “fix the crisis in social care once and for all”.

The failure to find agreement is nothing new, however, with the issue having defeated Labour and Tory administrations for close to 25 years. The costs will only become more acute as the vast baby boomer generation ages.

Ten years on from his landmark review, Sir Andrew Dilnot said on Wednesday that the failure to follow through with reform was a “stain on our nation”.

Four key areas of tension between Johnson and Sunak remain.

Insiders say Johnson was soon persuaded of the need to cap private social care costs once he became prime minister. The cap is not designed to help the poor, but to bring relief to any family that is unlucky enough to be hit with catastrophic costs, normally resulting from long-term chronic illness such as dementia or arthritis.

Since private companies have been unwilling to insure against these risks, the question is whether the state should mandate a form of social insurance. In 1911, Winston Churchill advocated social insurance for rudimentary disability support “to bring the magic of averages to the aid of the millions” and Johnson is keen on emulating his hero in social care.

The question is the right level of the cap. At roughly £50,000, the annual cost would currently be roughly £3bn, but the Treasury is keen on a figure of £100,000.

At the higher level, many middle-income families would still lose all their assets, including their homes, to care costs. The Treasury declined to comment.

Dilnot’s plan envisaged both a cap and a more generous means-testing arrangement for the poor. Currently individuals have to fund their own care costs if they have assets worth more than £23,250 and the plan proposed raising that limit to £100,000.

However, as with the cap, the Treasury is resisting protecting housing wealth in that way, aware it would make the policy hugely more expensive to deliver.

One person familiar with discussions said: “The Treasury thinks there is money there that can be unlocked”, adding there were legitimate concerns about how casting the means-testing net so wide would affect “the redistribution of capital and levelling-up. There are some arguments to be made by the Treasury that do have political as well as financial salience.”

Sunak, according to officials, argues that the public finances are already under intense strain, while tax levels are the highest since the late 1960s. “Rishi’s point is the money has to come from somewhere,” said one.

One person briefed on the talks between Johnson and Sunak confirmed that a “social care tax” was being considered alongside the Dilnot model.

Number 10 insiders insisted such a tax was “not the focus of discussions”, but some Treasury veterans — including former permanent secretary Sir Nick Macpherson — are coming around to the idea.

Even if the government reaches agreement on a cap-and-floor model, the broader underfunding of the sector and low levels of pay for staff will remain unaddressed.

The Department of Health and Social Care said it was committed to improving the system and “will bring forward proposals this year” to put it on a “sustainable footing” for the future.

Throughout the pandemic, it had provided almost £1.8bn for adult social care including infection prevention and control measures, it said.