Unlike his predecessor, Rishi Sunak has made it to 100 days as prime minister – but with problems mounting up in his in-tray.

Are they surmountable? Downing Street insiders insist he has done a lot in this time and point to his key achievement as fixing the mistakes of the Truss administration, which sent the pound tumbling.

The Autumn Statement, with £55bn of tax rises and spending cuts, has “brought mortgage prices down and prevented people losing their homes”, says a Number 10 source.

“We have set out plans for immigration and NHS recovery, brought forward minimum service and protest legislation, and he’s made an impact on the world stage”, they add.

But weeks of industrial action have taken a severe toll on the health service and contributed to the impression that, from the railways to the postal service, many aspects of daily life are creaking at the seams.

He may also be on the brink of losing a third cabinet minister to scandal, with mounting complaints against deputy prime minister Dominic Raab, following the departures of Nadhim Zahawi and Gavin Williamson.

The polls are also grim, not just for the Conservatives – consistently some 20 points behind Labour – but also for Sunak personally, making Conservatives jittery about whether he is the man to turn their fortunes around.

Although he scores better on “trust” and “competence” than Liz Truss or Boris Johnson did by the end of their tenures, the number of those polled by YouGov this month who would choose Sunak over Keir Starmer as prime minister is just 22%.

The positive spin, by Rishi Sunak’s allies, is that the problems with cabinet ministers are “legacy issues”, as one MP put it, and will be forgotten in a few months when they also hope inflation falls and strikes peter out.

Then, they hope, he can take the fight to Sir Keir Starmer and deliver on his recent five promises. 

But plenty of Tories worry that the priorities he set out at the start of the year – on inflation, debt, growth, the NHS and small boats – even if other events do not derail them, are just too limited.

Some in the party worry there is no message to young and middle-income families who can’t afford to buy or rent a home, after Conservative MPs rebelled over house building targets last year.

A former cabinet minister who backed Sunak tells me he “inherited a horror show and has calmed it down” but warned that he lacks an inspiring vision and “needs some luck with no more scandals.”

There are also divisions in the party on key issues – notably whether the prime minister should cut taxes this year with the low-tax right of the party putting the pressure on, ahead of the March Budget. And any decision on the Northern Ireland Brexit arrangements will need careful handling.

The next election is likely to be almost two years away, and polls can narrow during the campaign – a Sunak ally points out that David Cameron’s Conservatives were 15-20 points ahead in the polls the year before the 2010 election and didn’t win a majority.

But with the local elections looming, a Conservative recovery still looks like a daunting challenge.