They usually fall out in the end. Prime ministers and chancellors, that is. The danger for Theresa May and Philip Hammond is that they fall out at the beginning. Recent history is littered with battles between occupants of 10 and 11 Downing Street who started off as close allies. Margaret Thatcher sacked Nigel Lawson (and her first Chancellor Geoffrey Howe); John Major dismissed Norman Lamont and Tony Blair and Gordon Brown arm-wrestled over when the Chancellor would take over.David Cameron and George Osborne were the exception. Like Blair and Brown, they had a joint political project, but were much better at resolving differences quietly. Osborne rightly thought the EU referendum could backfire, but kept his doubts private. May and her Oxford University contemporary Hammond are not as close as Cameron and Osborne. Her Chancellor does not attend the morning strategy meeting of her tight inner circle, as Osborne did under her predecessor. But Hammond fights his corner in Cabinet committees, watering down some of May’s ideas on tackling the worst excesses of capitalism – curbing executive pay; putting workers on company boards and limiting foreign takeovers. He gained May’s respect by not leaking his victories, but their relationship was workmanlike rather than close.Now it is going to be tested to the limits. The Prime Minister has hinted at a retreat over his key Budget measure to raise National Insurance contributions (NICs) for the self-employed. She defended the policy but, in the face of a serious Tory backbench revolt, suggested the pill would be sugared with new rights for the self-employed, perhaps on parental leave and pensions. The NICs change may also be tweaked to reduce the income loss for the “ordinary working families”. The Prime Minister cannot afford to alienate the very group she champions. An inevitable blame game has begun into how a supposedly cautious Budget has boomeranged, and put May on the wrong side of her cheerleaders in the right-wing newspapers for the first time since she entered Downing Street.May allies cannot believe that the Treasury team so underestimated the backlash over breaking the pledge in the Tories’ 2015 election manifesto not to raise income tax, National Insurance or VAT. They think Hammond acted more like an archetypal Treasury official than a politician. In turn, Hammond supporters insist that No 10 was fully aware of the change. They are sniffy about what they regard as the anti-business, soak-the-rich instincts of May’s close advisers, who wanted to see higher rate taxpayers to be hit harder by the NICs shake-up. MPs close to Hammond believe the May camp does not fully appreciate the need for Britain to be “open for business” in the post-Brexit era. The Treasury sees itself as the department for blocking bad things proposed by others. But this time it has messed up.There is undeniably a strong case for the NICs change on economic grounds. The rapidly rising ranks of the self-employed cost the Treasury £5bn a year through lower tax revenue, something it can ill afford when coping with clearing the deficit, from the rising number of elderly and the cost of Brexit. But the politics of it were naive.The NICs rise would not take effect until April next year. So May allies wonder why the Chancellor did not delay the announcement until his Budget in November. By then it could have been part of the Government’s response to a review of the changing labour market by former Blair aide Matthew Taylor. May has already hinted that this will lead to greater protection for workers in the gig economy.The Hammond camp replies that May wanted him to find extra money for social care, easing the pain of business rates rises and her pet project on grammar schools. So he had to say where the money would come from. Hammond paid a price for his fiscal rectitude. Osborne would probably have funded these commitments from “money down the sofa” – the higher than expected tax revenues since November. Not Hammond.The Treasury’s immediate response to the row was poor. Rather than claim on a technicality that the manifesto pledge had not been breached, it would have been better to fess up. The Treasury should have argued that we are in new times, pointing out that the much bigger pledge to run a budget surplus by 2020 was ditched after the Brexit vote.There are also differences between May and Hammond over Brexit. The Chancellor would have preferred not to rule out single market membership and fought a rearguard action for the UK to stay in the customs union. He lost.May and Hammond will need to learn lessons from this week’s disaster; history tells us that chancellors and prime ministers sink or swim together. May needs Hammond more than she might realise.The truth is that both Nos 10 and 11 are culpable for the debacle. One probable cause is that May does not really feel bound by the Cameron-Osborne manifesto. But she can’t have it both ways; she stood on the same programme in 2015 and if she wants to start a new government, she should seek a general election and win her own mandate.