Today's inflation figures underscore that the economy is the biggest challenge facing Andy Burnham.

It is only 42 days until John Healey's first Budget, and there is increasingly apparent concern at all levels of the government and Labour Party about how that Budget can – or, as it may prove, cannot – substantiate Burnham's rhetoric about offering the biggest change in British politics in 40 years.

Much of the tricky economic environment, yes, is driven by global factors including the persistence, and to some degree worsening, of the conflicts in the Middle East and Ukraine.

And the AI boom pushing up borrowing costs is another issue affecting many countries.

But there are clearly domestic factors particular to Britain, and on that front it was very striking to hear the former Bank of England chief economist Andy Haldane telling LBC on Tuesday that without signs of cuts to public spending "the markets now suspect that this is a traditional tax and spend socialist government with better TikTok videos".

From somebody who at times has informally advised Burnham's operation, that will sting, not least because a similar criticism has been voiced in recent weeks by the prominent economist Lord O'Neill – another sometime adviser.

The prime minister gave a direct response to Haldane, saying: "That doesn't tell the story. We are not that."

Andy Haldane's criticism of Burnham's economic approach carries extra weight, given his role advising the PM

He identified "putting digital ID on hold" as an example of how he had already "taken difficult decisions in this job in relation to reprioritising government spending" and vowed to continue to "take difficult decisions to make sure the economy remains on track".

Digital ID is a striking choice of example. Burnham announced that he was abandoning the scheme in the days before he became prime minister so that he could focus on policies affecting the everyday cost of living.

But the spending was then, within the new government's first few days, re-allocated to cut VAT on household electricity bills.

So in that sense it was not a reduction in public spending, just a reprioritisation. And in any case, the former cabinet minister Darren Jones criticised Burnham at the time on the grounds that the government had not yet allocated the money for digital ID.

Certainly the signs from Healey's first major speech as chancellor last week were that he wants to reassure the markets, promising to "control public spending" and praising Rachel Reeves for beginning to "recover Britain's fiscal discipline".

Burnham and Healey would hardly be the first PM-chancellor double act to adopt different tones and emphasise different priorities in their public appearances.

As a junior minister at the Treasury almost 25 years ago, Healey was engaged in the question of how to boost growth around the country, long before it became central to Burnham's vision for Britain.

But there are people in government who are beginning to wonder whether their economic visions are quite as aligned as expected. "It's what everyone is thinking and some of us are vocalising," one government source said.

There are also those who fear the adverse political consequences of a Labour government seeking to go out of its way to demonstrate its fiscal credibility. Arguably that was behind the removal of the Winter Fuel Allowance for most pensioners as one of Sir Keir Starmer's first acts, an early factor in his political demise.

For Labour's political opponents, all this amounts to a question of whether the prime minister is willing to disappoint his own MPs. Yet it's worth remembering that with winter fuel the frustration in parliament was primarily caused by the furious reaction of Labour MPs' constituents.

Arguably this presents a more fundamental tension: are the kinds of policies needed to soothe the markets politically deliverable given Labour's electoral coalition and its need to shore up the 'progressive' vote?

The Budget is only six weeks away and will be the first and most important sign of the new government's answer to that question.

Chancellor calls for 'confidence about Britain' despite 'historic high' borrowing costs

Burnham refuses to rule out tax rises in autumn Budget

Call to raise tax thresholds among union demands ahead of Budget

Sign up for our Politics Essential newsletter to keep up with the inner workings of Westminster and beyond.