It is one of the more endearing eccentricities of British government that the two most powerful people in the cabinet live next door to each other. Even more bizarrely, they also live on top of each other, since the chancellor’s flat is located above Number 10 and the prime minister’s living quarters are above Number 11.

When Theresa May and Philip Hammond first moved in, one veteran official hoped for “a long overdue restoration of some normality” in the relationship. For two decades of Westminster’s version of Neighbours, the soap opera has been either a love-in or a punch-up. Neither was an optimal way of governing.

With David Cameron and George Osborne, the problem was over-intimacy. George was forever popping through the communicating door between Numbers 10 and 11 for a huddle with his great mate Dave. This closeness had its advantages. They didn’t row often and when they did were generally careful not to quarrel in front of the children. Mr Osborne loyally threw himself into the Brexit referendum, even though he had privately – and, as it turned out, correctly – told his chum that it was a reckless gamble that could do for the both of them. The great flaw of the Camborne relationship was that they were far too alike in their backgrounds and the way they thought. Blunders such as the infamous omnishambles budget might have been avoided had there been someone in the room acquainted with the large section of the population that likes a hot pasty.

It was a different story with Tony Blair and Gordon Brown. That was a saga of comradeship that curdled into a bitter enmity, mainly sourced in the chancellor’s obsession with replacing his next-door neighbour. “Give me a fucking date” was one of his subtle ways of pressing his claim to take over. The rivalry had advantages when it led to rigorous scrutiny of policy ideas – both Number 10 and the Treasury had to raise their game – but government was too often paralysed by the fratricidal struggles between the duo at the top.

Theresa May and Philip Hammond both arrived in parliament in 1997 and so both have been eyewitnesses to what can go wrong with this most critical relationship. Both set out with the goal of having a friendly but businesslike approach to each other. They would find a middle way that avoided the uncivil wars of Blair and Brown and eschewed the cloying closeness of Cameron and Osborne. They would aim for a relationship that was not too hot and not too cold, but just right. Just right is what it absolutely needs to be when they will be jointly responsible for the peril-strewn task of removing Britain from the European Union while administering more austerity for years to come.

They may have set out with good intentions, but what is it that they say about the road to hell? Even before the self-imploding budget, strains were beginning to show. Mrs May arrived at Number 10 with a deep suspicion of the Treasury. That distrust was encouraged by her chief ideological guru, Nick Timothy, a man who has long believed that Mr Hammond’s department is over-mighty. The hostility has been sharpened by the chancellor’s determination to shoot down Number 10’s attempts to make good on the PM’s promises to fashion a “different kind of Conservatism” that reforms capitalism, spreads its fruits more widely and tempers corporate behaviour. The chancellor has resisted the prime minister on curbing excessive executive pay and giving workers representation on boards. This naysaying is the more resented because the Treasury has a way of representing its role as vetoing “silly ideas” from Number 10. No one likes to be called silly. Prime ministers and their senior advisers really don’t like to be called silly. Mr Timothy has been strengthened in his conviction that the chancellor’s empire needs taking down a peg or five. “Nick can’t bear the Treasury,” says a senior Tory who knows him well.

From the Treasury comes the complaint that Number 10 is blasé about the grave hazards to the economy posed by Brexit. In sneers loud enough to be heard over the road, Treasury officials scoff that Mrs May is a “Home Office” prime minister, surrounded by people fixated on immigration and who wouldn’t know their GDP from their CPI.

Those tensions have been dramatically ratcheted up by a budget that has exploded in the faces of both the principals. I groaned when Tim Farron dubbed it the “omNICshambles”. But credit where it is due to the Lib Dem leader: his mocking label has been widely adopted. The proposed increase to the national insurance contributions paid by some of the self-employed has brought together a potent combination of opposition from the press and the Tory backbenches. For the first time, Mrs May finds herself on the wrong side of rightwing papers that previously adored her. She will also be disturbed that this issue sees Conservative MPs on the right rebelling in alliance with some of its liberal wing, for whom it is a way of getting back at the prime minister for other things they don’t like about her regime.

Facebook Twitter Pinterest Theresa May said a manifesto promise over national insurance was not broken. Photograph: Isopix/REX/Shutterstock

It is not uncommon for a budget to provoke backbench mutiny and media hostility. What is telling about the relationship between the prime minister and chancellor is how they have handled this first episode of serious adversity. Rather than stand firm and together in the face of the storm, they have allowed a blame game to start. On the evening of budget day, by which time they had begun to appreciate how much trouble they were in, Mrs May’s people attempted to channel all the opprobrium in the direction of Mr Hammond. They pointed the finger at him for not spotting that the tax hike would bust a manifesto pledge, a trap concocted by George Osborne as a way to snag the Labour party that has ended up biting the legs of the Tories. Adversaries of “Spreadsheet Phil” say that this demonstrates that proficiency at accountancy is not enough in a job that also requires acute political antennae.

The defenders of the chancellor retort that it is the prime minister’s fault for demanding that the Treasury scrabble together extra cash to buy off trouble in this area and that. Some mutter darkly that Mrs May is not as steely as she likes to look and wilts under pressure. The money had to come from somewhere and Number 10 was kept fully in the loop from the start. “Nothing was hidden from them,” says one ally of the chancellor. Indeed, unless there is no one employed at Number 10 to monitor the media, it is hard to see how they could have been ignorant because this tax hike was heavily trailed well in advance. The truth is that both addresses are to blame for not anticipating the grief this would cause them. It is the product of a shared complacency induced by the absence of effective opposition from Labour. It is also the result of a mutual belief that they represent a new government, so that promises made by the previous management don’t really count. But those promises do count, because Mrs May and Mr Hammond were elected on the Tories’ 2015 manifesto, a document that four times and without qualification pledged not to raise national insurance contributions. They have collectively made things worse for themselves by contending that this is not a breach of a manifesto pledge when it so blatantly is. If there is one thing more infuriating than someone who breaks a promise, it is someone who breaks a promise and then tries to pretend that they haven’t.

Mrs May could seek release from that manifesto’s promises by trying for an early election in which she could ask for a fresh mandate under her own name. As I revealed to you last week, a growing number of Tory MPs reckon their leader is mad and maddening for ruling out an early election. Since I reported that, William Hague, the former foreign secretary, has become the most senior Conservative to go public with the call for the prime minister to take this course.

One member of the cabinet who is close to the prime minister recently told me why he and she think a snap election is a bad idea: “It would trash her brand.” Mrs May has built her approval ratings on a reputation for being a solid person who can be relied on to stick to her word. This, I suspect, is what most concerns the prime minister and her people about the budget. It certainly ought to worry them. Busting a manifesto pledge, and then trying to pretend that you haven’t, is damaging for that May brand. It looks exactly like the sort of untrustworthy games playing that she is supposed to abhor. For the chancellor, fumbling his first budget is clearly corrosive of the Hammond brand, which was centred on the notion that he is a safe pair of hands.

As for their future together, a relatively light stress-test of the relationship has exposed serious tensions between the Downing Street neighbours and their teams. Ahead lie the far more pounding pressures that will come with the momentous challenge of negotiating Britain out of the European Union. They haven’t even embarked on that hazardous journey and the cracks are already beginning to show.