Prime Minister's Questions: new politics means paying attention at the back

We had teachers like Jeremy Corbyn at school. They didn't want any mucking about because we were there to learn and they were there to teach. We would size them up and if they were weak we would destroy them. We would have noticed Corbyn jiggling his knees before the class started, with his sheets of paper on a red wallet folder on his lap.

We would have been briefly silenced when he said, more in sorrow than in anger, "It might be funny to some people but it's not funny to Matthew." Matthew was the person on above median income who couldn't afford to buy a house in London. We would be slightly embarrassed, because Corbyn was after all asking serious questions about serious subjects. We even agreed with him about the cuts to Kelly's tax credits. She's a single mother with a disabled child who is going to lose £1,800 a year. In fact, we agreed with him so much that we shouted, "Shame! Shame!"

Which only gave David Cameron the chance to show that he could do injured innocence and moral superiority better than the new supply teacher. "Sorry? What happened to the new politics?"

Mostly, Corbyn did the new politics very well, but he threw it away on detail on both tax credits cuts and on housing, his two big subjects. On tax credits, he patronised Cameron cuttingly, as a poor teacher would a pupil too pleased with himself: "The Prime Minister is doing his best and I admire that." But then he said: "Inequality is getting worse not better." This is a disputable point – incomes have become slightly more equal in the past few years, while the evidence on the distribution of wealth is mixed – and the Prime Minister disputed it. "His figures for inequality are simply wrong."

If Corbyn had said that cuts to tax credits would increase inequality in future, he would have been pressing Cameron on his weakest point. As it was, Cameron could do the new politics all day and with one bound was free.

The same happened on housing, which is a complicated and probably insoluble problem. Corbyn didn't have a question, except the general, "What is he going to do about it?" For someone with a decade's experience of PMQs, that was too easy. "We built more houses in five years than the previous Labour government did in 13."

Still, Corbyn had one "new politics" device that worked brilliantly, and that was to use his sixth question to change the subject. He asked a serious question about secondary breast cancer. That prevented Cameron from holding back until his sixth reply to deliver his best put-downs. Instead, he was forced to agree with the Honourable Gentleman – as he called Corbyn carefully throughout, to draw attention to his refusal to join the Privy Council, on which he would become a Right Honourable Gentleman.

After that, Cameron was liberated to let off some steam by kicking Angus Robertson, the Scottish National leader, around a bit for asking insufferably sanctimonious questions about foreign policy. "Would he be happier with Gaddafi still in power?"

And he was able to relax into the old politics a bit more with the rest of his answers, in which he sounded ever more like Tony Blair. When Nigel Huddleston, a Conservative, asked about the new national infrastructure commission, Cameron praised Andrew Adonis, the Labour peer who will chair it. Labour MPs, much happier with the old politics of barracking, shouted that this was a “Labour policy”. Cameron stopped, with a Blairite "Yeah?" He turned to them: "Where we find a good Labour policy, we implement it. And tonight we will be voting for something that until last week was Labour policy," he said, referring to the Charter for Fiscal Responsibility, for which John McDonnell, the shadow chancellor, intended to vote until yesterday.

He was enjoying himself, and became quite indignant with the Speaker, who cut him off: "The Prime Minister has finished his answer."

Everyone has to pretend that Corbyn's new way of doing PMQs is much better than the yah-boo of yore. I'm fine with it, as a policy geek. But it will work only if both sides of the classroom respect the new teacher.