Even if Jeremy Corbyn were a much more adept parliamentary performer, today’s prime minister’s questions would have been a tough fixture. And so it proved.

Theresa May arrived in the Commons off the back of a personal success in her Brexit speech yesterday. It was full of claims that may not survive contact with the other member states – it called to mind Mike Tyson’s comment that all his opponents had a plan “’till they get punched in the mouth” – but there is no denying that it was a personal success, got good press reviews and pulled her party together. Everything about May’s demeanour today was that of a prime minister with fresh authority.

Corbyn’s problem was that he had no alternative but to question May about Brexit. This isn’t the Labour leader’s specialist subject on any day of the week, but it was the subject of the day. He would much prefer to talk about the NHS crisis – as several backbench MPs on both sides of the Commons did – but as leader he was compelled to come out of his own comfort zone.

He chose to do this by talking about parliament’s role. How could the prime minister who makes such a fuss about British parliamentary sovereignty when talking about Brexit not have given her speech in the Commons, he asked. The question set Corbyn up for the kind of Commons joke that he is hopeless at. Not the iron lady but the irony lady, he called her. It fell as flat as a bad performance at the Glasgow Empire.

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In fact Corbyn is on to something here, but he failed to make the most of it. He should have pressed May on her refusal to publish a white paper on the issue, instead of just giving the speech. He could have tried to get her to issue the speech as a white paper, which is what parliament seemed to expect after the Labour-initiated Brexit debate in the Commons before Christmas. Crucially, this was an issue on which the backbench Tory pro-Europeans Anna Soubry and Ken Clarke pushed back against May yesterday. If Corbyn had set up a pincer movement – perhaps even enlisting the SNP too – he might have won a skirmish.

Instead he simply did what he always does. He pressed on with his scripted questions instead of trying to come back at May for her replies. No one pretends this is an easy skill to master, and Corbyn is far from alone in his inability to think on his feet in the Commons the way that others (not including May, generally speaking) often can. But he needs to think in terms of winning positional victories – as the SNP’s Angus Robertson sometimes does – rather than lecturing May about his own virtuous view of the world when compared with hers.

It all doomed Corbyn to a pretty miserable session, in which he got some of his facts wrong and in which May was able to treat him with a contempt that isn’t pretty, but which accurately reflected the fact that, when it comes to Brexit, she knows what she wants and Corbyn doesn’t really know what he wants. And it showed.