After a bruising week for the government, with backbenchers unhappy about sleaze and watered-down rail plans, the prime minister’s authority will be tested again this week.

The Health and Social Care Bill is back in the Commons and the fine-print on the social care cap has come under criticism.

Under the new plans, from 2023 personal care costs in England – for things such as washing, eating, and dressing – will be capped at £86,000.

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Once that amount is reached, care is paid for by local authorities.

But this week the government confirmed that means-tested support payments from councils will not count towards that cap, which means poorer pensioners could have to pay more before the government steps in.

Critics blame the government of favouring wealthy pensioners and the Treasury of cost cutting, arguing the cap impacts people with less valuable assets and will disproportionately affect those living in the north of England.

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The government says the new system will be fairer and more generous, but one Tory MP described the mood on the backbenches as “angry and rebellious”.

There is no expectation of a government defeat, but there is unease and concern among backbenchers, including senior Tories, and some are poised for rebellion.

The government knows that politically, for a prime minister who pledged to fix social care, what happens next could be seized on by Labour as another broken promise.