An unwritten law of Westminster mechanics states that power, in the absence of a countervailing force, gravitates to the Treasury.

The governing agenda can be set in No 10, but a prime minister has few instruments of control as immediate and far-reaching as the purse strings in a chancellor’s hand.

It is the difference between Keir Starmer speechifying solemnly on the need for difficult choices and Rachel Reeves scrapping winter fuel payments for millions of pensioners. There is no discrepancy in the position but a clear disparity in impact.

When dozens of Labour MPs abstained in a Commons vote against the cut yesterday, their quarrel was with the Treasury’s precise implementation of the prime minister’s loose prescription. It was tame, as parliamentary rebellions go. The government whips won the day. But so much queasiness so early on in the journey does not bode well for a government that is promising many more hard yards before good times come into view.

Dissent is deferred, not dissolved. Labour MPs have been told not to expect any retreat from austere decisions, but a prolonged backlash could still necessitate palliation for the neediest pensioners.

Alongside quibbles with the policy, there is disquiet about the tone of the government’s message. Labour MPs accept that the grim Tory inheritance demands a sombre conversation with voters but wish the mood music could be less funereal.

A tonal adjustment is due at the party conference later this month. The Labour leader’s keynote address has to be upbeat, arranging short-term privations in a narrative arc pointing to a happier horizon.

But the government’s fortunes depend a lot less on what Starmer says in Liverpool than on what Reeves does with her first budget six weeks later.

That set piece, the ritual funnelling of all economic policymaking into a single speech in the Commons, is a major source of Treasury power. It forces every other cabinet minister into weeks of supplication before the chancellor. She then has a special day set aside in the Westminster calendar to dictate the terms of political debate for the ensuing year.

The pattern is baked into British political convention. It is intensified in the current government by three factors.

First, commitment to budget discipline was the fulcrum around which Labour turned its electoral fortunes in opposition. It was central in the campaign to win back public confidence. That installed Reeves as the gatekeeper for manifesto pledges and embedded the shadow Treasury team in positions of structural primacy before they arrived in office.

Second, Starmer is not an economist and is happy to delegate number crunching. That isn’t a failing. Prime ministers who try also to be their own chancellors get bogged down and end up fighting the person they appointed to do the job properly. Managerial detachment is one of Starmer’s strengths. He is still the author of Labour’s political strategy. But no one imagines that a measure like cutting winter fuel allowance came out of a drawer in No 10.

It is a textbook case of Treasury brain. This is the notorious syndrome that causes clever officials in Whitehall’s smartest department to identify cost savings that look ingenious on a spreadsheet but turn out stupid in the real world. (A famous outbreak, featuring the imposition of VAT on hot takeaways and static caravans, led to the unravelling of George Osborne’s “omnishambles” budget in 2012.)

Treasury brain means prejudice in favour of any action that promises immediate cash for the exchequer and suspicion of any proposal that incurs cost upfront, justified with hypothetical revenues somewhere down the line.

Sometimes that caution is reasonable. But it militates against long-term investment and spending on unquantifiable public goods – preventive healthcare, say, or prisoner rehabilitation – that can save money for future chancellors by reducing the bill for social decay.

That points to the third reason for likely Treasury dominance in the coming years. Whatever else Starmer imagines he might do with his first term in office, this parliament will be largely defined by competing pressures – to plug holes in the public finances and repair public services.

The dilemma is mostly a legacy of Tory mismanagement but sharpened by Labour’s pre-election tax and spending commitments. Reeves acquiesced to budget constraints set as a trap by a Conservative chancellor who expected to lose an election and knew the impossible task of implementation would be someone else’s problem.

Future historians of the Starmer project can debate whether that compromise was necessary to neutralise voter fear of Labour profligacy. The only scenario we have is the one where the plan worked. No one knows whether the same would have been said of a manifesto that promised to reverse Jeremy Hunt’s national insurance cuts or left open the option of income tax rises.

Reeves’s allies are entitled to feel some frustration at critics whose alternative plans amount to variants of the old recommendation not to start from here. It is easy to find fault with any particular measure, lamenting the cruelty and short-sightedness of each cut. It is easy also to presume that somewhere there lurks a more deserving target. Saying who that should be is the hard bit.

But the winter fuel cut has also drawn criticism from Labour MPs who want to be loyal to Reeves and Starmer. Their complaint is that it undermines a story the government wants to tell about placing the greatest burden on those “with the broadest shoulders”. It is true that plenty of wealthy pensioners, millionaires among them, don’t need their annual energy subsidy. But there are still poorer ones who do.

This will be a recurrent problem. There aren’t enough super-rich people to tap for all the necessary tax receipts. Everyone else can see someone whose shoulders look broader than their own and resent their share of the burden. The big revenue-raising levers – national insurance, income tax, VAT, corporation tax – are the ones Reeves has promised not to pull.

The chancellor could also borrow more money, eking out some flexibility in the small print of the fiscal rules she has drafted for herself. But there is a limit, and no one wants to probe it. In highly turbulent times, the Treasury’s morbid terror of some unexpected shock triggering a global debt crisis is not irrational.

So there will be a lot of scraping around for cash through cuts that end up having to be reversed or mitigated with ad-hoc pots of compensation. The Treasury brain will conjure up myriad fiddly tax rises with perverse unintended consequences, whipping the targeted group into a frenzy that does political damage out of proportion to the sums being collected.

Starmer, having happily delegated economic policy, will find himself spending a lot of time managing rows that were not made in No 10. Although he is committed to a long-term strategic model of government, ending what he calls “sticking-plaster politics”, he has signed up to a fiscal strategy that could require their frequent application.

By all accounts, Starmer and Reeves enjoy a solid and healthy professional relationship. It may well prove resilient in the years to come. But it is about to be stress-tested under an immense mechanical force that has caused many a partnership between prime minister and chancellor to come unstuck.

• Rafael Behr is a Guardian columnist