Jeremy Corbyn has decided that doing politics differently didn't really work, so today he did it the same. He picked a weak argument of the Prime Minister's and devoted all six of his questions to it.

Question five featured the briefest of tributes to his old "people's question time" idea, like an ageing rock star throwing in a riff from his early experimental music, as Corbyn quoted four Year-6 pupils at a primary school in his constituency. But as their question to David Cameron was merely, "Why are you doing this?" Corbyn felt the need to back it up with a quotation from Kenneth Baker, the Conservative former Education Secretary.

As a result, Corbyn had one of his best outings as Labour leader. Cameron wasn't embarrassed as such – shamelessness being one of the qualifications for high office – but he transparently failed to produce any argument for the policy of forcing all schools to convert to academies.

Corbyn cleverly labelled the policy a "top-down reorganisation", making the analogy with the pointless and unpopular changes to the NHS made in Cameron's first term. Cameron responded with meaningless statistics, saying that 88 per cent of converter academies are rated good or outstanding, which any Year-6er would know was proof of nothing at all.

In the end his only argument was that academies are "true devolution", which is like saying people shall be forced to be free. The strongest supporters of academies are likely to be dismayed by the policy of compulsion, which is the one thing guaranteed to destroy the possibility of persuading the doubters, especially when the evidence on standards is not yet conclusive.

That is why academies – rather than today's rise in the jobless numbers – was the right choice for Corbyn's attack. In the end, all Cameron could manage was a couple of feeble jokes about McDonald's. He pretended he had misheard that Labour was banning McDonnell, "but it was not the job destroyer, it was one of Britain's biggest employers", and concluded by saying, "I'm lovin' it."

From that gruesome line the session was all downhill, as Tory anti-EU MPs asked hostile questions about the referendum campaign. Christopher Chope asked about the 3m net immigration forecast by the Treasury in its report designed to warn of the costs of leaving the EU. We just copied out our homework from the Office of Budget Responsibility, said the Prime Minister. Charlotte Leslie asked if his friend Angela Merkel was "outstripping everyone in making the case for Brexit". Cameron's reply was along the lines of no.

At last the unlikely cavalry arrived in the form of Kenneth Clarke, inviting Cameron to hold a seminar for "respected colleagues" on "the nature of international trade", because some of them (naming no names, Michael Gove) seemed to think "you simply have to turn up anywhere in the world and sell goods and services that comply with British rules".

With the London mayoral election just two weeks away, the session also featured electioneering of the crudest kind, as the Prime Minister accused Sadiq Khan, Labour's candidate, of sharing a platform nine times with a man who "supports IS". Corbyn shouted "Disgraceful!" from his seat, but the link between a Muslim candidate and someone who allegedly supports the Islamic State was made and cannot be unmade. Let us hope that this is a sign of desperation, because Khan is so far ahead in the London race.

For once, though, Corbyn could leave the Chamber thinking that he had done a good job of holding the Government to account. It was unlikely that Cameron could get the forced academies policy through the House of Lords in any case, and today's exchanges may have helped to force another U-turn.