Jeremy Corbyn deployed some sophisticated tactics for the last Prime Minister’s Questions before the referendum. First, he caught his opponent off guard. The Leveson inquiry into press ethics must have been the last subject David Cameron expected for the first question.

You could almost see the Prime Minister thinking, “Leveson: that name sounds familiar; don’t tell me he’s waded into the Brexit debate?” But no, Corbyn merely wanted to know what had happened to the second stage of the Leveson inquiry, and would Cameron meet some of the victims of phone hacking.

The Labour leader also accused some of the Prime Minister’s Brexit-supporting colleagues of “cosying up to Rupert Murdoch”, meaning that he had noticed that The Sun came out for Leave on Tuesday. Cosying up to Murdoch is one of the war crimes of which Tony Blair is supposed to be guilty, so perhaps Corbyn was trying to be helpful to Cameron by attacking Conservative Leavers in such extreme terms.

The Prime Minister didn’t seem entirely sure, so he played it safe. The second stage of Leveson was always going to be after the criminal prosecutions had been completed, but they are continuing, he said. He had met some of the victims of phone hacking. And he added: “People can accuse me of many things but cosying up to Rupert Murdoch isn’t one of them.”

Such defensiveness was a sure sign that Corbyn’s cunning plan had unsettled him.

Corbyn’s second question was about whether Boris Johnson and Michael Gove wanted to privatise the NHS. They are “wolves in sheep’s clothing”, he warned. He contrasted them with a Tory in Labour clothing, Sarah Wollaston, who had changed sides from Leave to Remain to defend the NHS.

Cameron looked for the catch, but he couldn’t see it, so he praised Wollaston’s bravery in changing her mind and said the NHS was safer in the EU.

Now Corbyn deployed the element of surprise again. He had asked about the EU posting of workers directive before at PMQs and got absolutely nowhere with it, so he asked it again. Would the Government outlaw agencies that advertise for workers only abroad?

The two MPs who knew anything about it looked at each other as if to say: They have, haven’t they? The rest looked at their shoes and thought, this is the last PMQs before the referendum: what is he doing?

Cameron was so thrown that he said nothing notable in reply. It was only in answer to Corbyn’s next question that the Prime Minister, having now been briefed, said that the Government was “looking to see if we can ban that practice”.

By then, Corbyn had changed direction again, the Muhammad Ali of PMQs, asking a question about the pressure on school places and on doctors’ surgeries – I assume from immigration but, just like the Prime Minister, I was finding it hard to keep up. Why was the Labour leader asking a Leave campaign question?

What we failed to realise was the subtlety of recognising Labour voters’ concerns about immigration in order to persuade them to vote Remain. Cameron managed to mention today’s record low unemployment figures, but Corbyn still had two more questions to go.

The Prime Minister’s head must have been spinning as he tried to work out from where the attack was going to come next. Up the Thames, it turned out. There is a flotilla of boats heading this way, said Corbyn. They are protesting about the EU, but is it not the case, he wanted to know, that it is the Government that is making it hard for them to get on with the job of “collecting fish”.

Corbyn the Fish Collector’s Spokesman was as unexpected as the Spanish Inquisition. Cameron’s mouth opened and closed as he gave an answer, but I made no notes.

Finally, Corbyn turned to the question of the referendum. MPs on both sides cheered happily, as this was what they had come for. “The Labour position is,” said the party’s leader as if he were talking about some people he had met at a funeral a few years ago, “that we’re going to be voting to Remain.”

He asked about the emergency Budget that the Chancellor said would be needed to rescue the public finances if Britain voted to leave the EU, and said Labour wouldn’t vote for more cuts. I don’t know what good it does the Remain campaign for the Chancellor to say Brexit would cause a fiscal crisis and Labour to respond, Oh no it won’t!

Cameron didn’t understand it either, and went into his prepared peroration. “There are few times when he and I are on the same side of an argument – that says something. This is a huge choice for our country.”

Thank goodness Corbyn so ingeniously caught the Prime Minister out, with eight days to go, in order to persuade a doubtful nation that the Tories are very bad and there are some people in the Labour Party who would like you to vote Remain.