Jeremy Corbyn has been fighting for his job for two years and it shows. He knows how to deal with the difficult questions now. The only moment when he paused and goggled was when he was asked about the Falklands. “I er wanted there to be a [cough] ceasefire,” he said, slowing down to a speed perilously close to Diane Abbott’s not-sure-of-the-numbers pace.

Jeremy Paxman had one embarrassing quotation from him in 1982 saying the war was a “Tory plot”, but Corbyn, picking up speed again, swerved back off the grass verge and onto the safe line of saying he wanted negotiations.

The Labour leader was even prepared to imply – although he didn’t quite say so – that he would be prepared to order a drone strike against a terrorist abroad who was planning a bombing campaign in Britain. After that he was back on track. His line on calling Hamas and Hezbollah his friends was rubbish – “I was using inclusive language in order to get a meeting under way” – but he has learned how to skirt around this one often enough now that he can do it without hesitation.

And then he was free. Paxman’s clever-clever decision to try to attack Corbyn from the left, for failing to get all the things he really believes in into the Labour manifesto, was a failure. It allowed Corbyn to pose as a consensual pragmatist who listened to his colleagues and worked with them, when in fact 172 of them said they had no confidence him less than a year ago.

Corbyn the Campaigner had handled the opening questions from the studio audience well. He even engaged with people who disagreed with him and urged them to change their minds. That sort of thing could never catch on, you know. The audience liked it, and so the gaping holes in Corbyn’s policies didn’t seem to matter much. He said immigration would “probably” come down under a Labour government “but I don’t want to be held to this”. Given what tribulations Theresa May was about to undergo on precisely this point, it seemed quite generous to let that go.

Then he tried to dodge Paxman asking why Labour would continue the freeze on benefits. He had tripped up on this at the launch of the manifesto, saying they wouldn’t be frozen under a Labour government, when there was no money in John McDonnell’s costings document to unfreeze them. So a spokesperson had to “clarify” that they would stay frozen. Now, after two turns of the Paxman rack, they were unfrozen again. Of course they would be uprated, Corbyn finally said. I don’t know if the spokesperson has clarified that one yet.

Then it was the Prime Minister’s turn. Her tactic with the audience was to try to bore them into submission. They didn’t like it much, but they accepted it from a woman who so obviously seemed to know what she was talking about. Joy, who asked what had happened to the £350m a week from Brussels, which was the only reason she had voted to leave the EU, even said she was happy with May’s answer, which was: “We won’t be sending vast sums to money to the EU and it is important that we get that best possible deal.”

The only point at which they rebelled was when she unwisely said Labour’s figures don’t add up. Which they don’t, as Corbyn had just confirmed, as if in passing. But someone in the audience shouted out that the Labour manifesto was “costed” and they all knew that there weren’t any proper numbers in the Tory manifesto.

Then she was into her grilling by Paxman, although, as with Corbyn’s, it was more of a wafting of warm supercilious air in her general direction. Whereas Paxman had attacked Corbyn from the wrong side, he couldn’t decide whether to attack her from the left or the right. He accused her of changing her mind on Brexit, which, given that she is a deeply sceptical Remainer who turned gamekeeper, was hardly the most wounding line of attack.

But Paxman couldn’t decide if she was favouring the rich by letting them pass on their wealth to their children, or fleecing pensioners by making them pay for their social care.

His most effective line was to accuse her of being a “blowhard who collapses at the first sign of gunfire” over her National Insurance U-turn. The audience liked that, but they also clapped happily when she said she had decided to call the election after saying she wouldn’t because other parties were trying to frustrate the will of the British people over Brexit.

And then she ended on her strongest subject: who do you trust to negotiate the Brexit deal. Paxman thought he had scored some debating point when she refused to say directly that she would “walk away” from the talks if she couldn’t get what she wanted, but all he had done was allow her to explain, with some force, what she meant by saying “no deal is better than a bad deal”. She said: “You are not in there to get a deal at any price.”