In order to reduce the cost of its new social care funding scheme for England by an estimated £900m, the government has opted to reduce the entitlement of less well-off people. Under the proposals put forward a decade ago by the economist Sir Andrew Dilnot, which ministers announced in September that they had decided to take forward, a cap on contributions will be applied. Set at £86,000, this becomes the maximum that an individual pays towards personal care, including that delivered in their own home (but not daily living costs such as food and heating).

The point is to protect the minority of people who need long-term social care, due to dementia or other illness, from the financial catastrophe of losing all their assets. Currently, there is no cap on the total cost of care home fees (or the cost of home visits). People who have saved all their lives in the expectation of leaving an inheritance to their children can be forced to sell their homes in order to pay to be looked after. The new social care system, which will be funded by a health and care levy added to national insurance contributions, will create what Sir Andrew calls a “national risk pool for social care” for the first time.

But the change in the rules that was announced last week is more than a technicality, and its effect is to make the scheme markedly less progressive. While the Dilnot cap would have applied to the amount spent on a person’s care, including contributions paid by councils on a means-tested basis, the government’s cap applies only to the amount paid out of private funds. The entitlement to means-tested support is effectively exchanged for support to cover costs over £86,000. Jeremy Hunt, the chair of the health select committee, called this “a really big disappointment” – but said that Tory MPs should vote for it anyway.

It is true that the revised plan remains preferable to no plan at all. But MPs and Lords should fight for further changes, in defiance of the government’s last-minute scrimping, and in the knowledge that a chorus of experts is on their side. All those with assets worth less than £186,000 will be worse off as a result of last week’s adjustments, and 60% of people who end up needing adult social care are in this group. For some of them, there will be only a marginal improvement on the current position; where a person’s assets must now be run down to the last £14,250 before state funding kicks in, in future £20,000 will be shielded.

Given the extent to which assets are concentrated in housing, and the huge variations in property values, geography is crucial. While a person in a £1m house will see 90% of their housing asset protected under the new scheme, owners of homes worth £100,000 stand to lose most of it. Labour’s Jonathan Ashworth has branded this differential impact “daylight robbery”. Sally Warren of the King’s Fund thinktank points out that Hartlepool, where the median house price is £128,000, was “the last red wall seat to fall”. The former cabinet minister Damian Green thinks that a fairer way to achieve savings would be to protect a “flat percentage of assets”, rather than creating a floor below which fees cannot be charged.

The critics are right. The government is wrong. If any of these poorer pensioners is forced to sell their home under the new arrangements, the Conservatives will break a manifesto promise. Boris Johnson talks of levelling up the north and shrinking the wealth gap between the English regions. But by its actions over the past week, his government has shown, once again, that its friends in the south come first.