A screeching U-turn, a climbdown, a budgetary black hole, a humiliation. It is hard to explain the bizarre events in the Commons on Wednesday as the prime minister toppled a key pillar of her chancellor’s week-old budget. The reversal was “announced” in a letter to the Treasury committee.

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The U-turn was on a proposed reform in that most arcane of fiscal realms, the national insurance contributions (NICs) regime. The change was to contributions paid by the self-employed, and seemed so uncontroversial that Philip Hammond was accused of forgetting to mention its significance when briefing cabinet colleagues.

More to the point, the change was modest and thoroughly sensible. Taken in conjunction with other NICs changes, it meant an average overall rise of £31 in contributions by those with profits of over £16,250 a year. Those with profits of under £15,570 would actually pay less. Even the highest earners, on profits of £45,000 and above, would pay only an extra £589 a year. It would start to close an emerging loophole in the taxation of workers in the so-called gig economy. It eased the impact on revenue of a drift into self-employment as tax avoidance. In general, it was a sensible and “progressive” tax reform.

The change was greeted with ritual objection by Labour and by small businesses affected, but with general acclaim by experts. The Institute for Fiscal Studies’ Paul Johnson called it “modest but welcome”. The government’s committee reviewing employment terms and conditions voiced its approval. The prime minister herself agreed, reiterating that the way self-employed people can use companies to avoid taxes paid by others was a loophole and unfair. The change would raise £2bn overall and thus contribute to the chancellor’s long-term aim of budgetary balance.

It was, in other words, a pretty straightforward measure. Unfortunately it conflicted with what the Tory party promised at the last election, which was not to increase income tax, national insurance or VAT. That promise may have been made by David Cameron and George Osborne. It may have been stupid, and it was certainly at odds with a stance of continued austerity. But it was a promise made, and Tory MPs who repeated it on doorsteps remembered it. They make many other promises with little hope of keeping them, but this was specific.

Thus “hitting” the self-employed was called an attack on the most enterprising and entrepreneurial sector of the labour market. The very core of the post-Brexit economy was being subjected to a fiscal kneecapping. As the storm grew last week, “concern” was expressed by no fewer than 18 Tory backbenchers; one more than May’s working majority.

It appears the prime minister did not even put up a fight. Within two days she bobbed, weaved and promised to stall the national insurance increase for “further consultation” and indeed for “review”, though there was no suggestion it would be abandoned altogether. The £2bn had to be found somewhere. That appeared to assuage the incipient backbench rebellion.

Then it was leaked that May’s aides were “furious” with Hammond, and indeed that 10 and 11 Downing Street were at loggerheads. Retaliation was in the air – and that is what May’s Commons performance on Wednesday seemed like. The tax increase was to be abolished. Last week’s tactical swerve was turned into this week’s abject climbdown. The occasion was relieved for May and Hammond only by Jeremy Corbyn’s ineffable ability to turn victory at the dispatch box into fumbling defeat.

Had May wanted to apply a political caveat to Hammond's budget, she had the opportunity to do so

May’s handling of this affair looks dire. Whether or not her chancellor had broken the letter of the manifesto – and he clearly broke the spirit – such breaches are hardly uncommon. May fought the election on the same manifesto. She was briefed and knew what was in Hammond’s budget. Had she wanted to apply a political caveat to it, she had the opportunity to do so.

More seriously, once such an announcement is made, collective responsibility would normally apply both to the policy and to the attendant political risk. The prime minister owes it absolutely to a colleague in trouble, whether with backbenchers or with the press, to back them up. This backing is not just for their benefit, but to reassure other ministers facing similar opposition to tough decisions in future. Last week’s partial climbdown was bad enough, but should have been the last word. To lead Hammond back for a second feast of humiliation was inexcusable.

For a prime minister so publicly to hang her chancellor out to dry, after a week of covert bad-mouthing, sets an appalling precedent. She may have intended to discredit him, but she discredited herself. She made him look foolish, and damaged his authority within cabinet and on the backbenches: in itself a dangerous move. But she devastated her position within the government as a leader prepared to stand up for what she believed was a sound policy in the public interest.

Many parallels are being drawn between May and her predecessor, Margaret Thatcher, sometimes to May’s advantage. At this stage in Thatcher’s leadership, in the 1980s, she was weak, fumbling and at bay. At least in the polls, May is strong. But Thatcher would have backed Hammond to the hilt. Her meticulous paperwork would never have allowed through a measure that she was not prepared to defend. She never indicated doubt over what she wanted to do.

If May could not have won a Commons motion on a 2% rise in national insurance – which is hard to believe – that would have been the moment to declare defeat, and light the blue touchpaper for an election. In the event, she showed herself (and her whips) to be a pushover for just 18 backbenchers with a lobby or a grievance. As we have seen with the “three aitches” – Hinkley, Heathrow and HS2 – May is putty in the hands of any costly pressure group that pops over the horizon and gets itself tabloid support. Her cursory treatment of colleagues might have worked at the Home Office. It will not work in Downing Street. If I was a Brexit minister just now, I would be trembling in my shoes.