Jeremy Corbyn is loved for his principles. So what happens when he has to play politics over Europe?

The Labour leader's speech on Europe today is an intriguing test of his consistency, sincerity and principle

Much rejoicing last night in Jeremy Corbyn's office, no doubt, at the YouGov poll in The Times suggesting that he is more trusted on the European Union than the Prime Minister. Asked, "Do you trust the statements and claims made by the following people on the EU", 28 per cent said yes, they trusted Corbyn, and only 21 per cent said they trusted David Cameron. This is a reversal of the position in a poll taken in the two days after Cameron concluded his EU renegotiation in February, when Corbyn was trusted by 26 per cent and the Prime Minister by 29 per cent.

None of these levels of trust is high, and it is pretty clear what has happened. Most Labour voters are pro-EU and assume that Corbyn is too. Most Conservative voters, on the other hand, want to leave the EU. Now that the inadequacy, in their view, of Cameron's renegotiation has sunk in, they have become less trusting of him on this question. This also explains Boris Johnson's better score, 26 per cent, although he has also lost ground since February from 34 per cent, because he has lost the one-third or so of Tory voters who support the EU.)

That assumption by Labour voters that Corbyn supports Britain's membership of the EU is what today's speech is all about. The poll is a vindication of Corbyn's decision to adjust his long-held Euroscepticism. Tony Benn's followers in the Labour Party have long campaigned for Britain to leave the European Community: it was Labour's policy in the manifesto on which Corbyn was first elected in 1983 and he refused until recently to accept Neil Kinnock's reversal of the policy.

If Corbyn had stuck to his Euroscepticism, the voters would have been confused and many of his enthusiastic supporters among the Labour Party membership would have been upset: they are all for traditional socialism, but they are also strongly pro-EU.

The tone of Corbyn's speech is unlikely to satisfy the more ardent supporters of EU membership in the party, however. Oliver Wright points out that, in the extracts released in advance, Corbyn talks about the Labour Party's position rather than “my position” and says, as if he were an independent commentator: “Labour is convinced that a vote to remain is in the best interests of the people of this country.” Although journalists were briefed in advance that the speech would be a personal account of the Labour leader's “journey” towards arguing for a vote to stay in the EU, it seems that it is no such thing.

At least the extracts contain no reference to TTIP, the Transatlantic Trade and Investment Partnership, the free-trade agreement that is being negotiated between the EU and the US. One anonymous Labour MP was quoted last week as saying of Corbyn: “When he finally gives this speech he has to be unequivocal – none of this TTIP rubbish, because it’s really starting to take hold in the debates I’m listening to among Labour members.”

It is on TTIP that Corbyn's balancing act becomes most precarious. He and John McDonnell regard TTIP as a capitalist conspiracy against everything that is good and pure in the world, and yet he has now decided to make the case that membership of the EU, although it is not perfect, is the best way to work within the system to improve it. Even if they do think that free trade is against the interests of working people, a position contradicted by the last 70 years of world history, their argument that the UK ought to work within the EU to improve TTIP is a persuasive one. Unfortunately, it doesn't persuade many of the activists in the Labour Party who are Corbyn and McDonnell's core power base.

When we finally get to see the whole of Corbyn's speech, it will be interesting to see what he says about TTIP, and whether he adds any genuinely personal touches to his account of his journey from wanting out of the European elite's club to his current position of working to make it more democratic and socialist from within.

Update: Well, Corbyn mentioned TTIP once, a curious single sentence, saying it was a "huge cause for concern, but we defeated a similar proposal before", the Multilateral Agreement on Investment in 1998. Similarly, he mentioned "austerity" only once, saying he wanted "economic reform" to end it, rather than portraying the EU as its engine.

The speech was effective, not least because Corbyn seemed cheerful and relaxed, possibly buoyed by the YouGov poll. It was a clever speech, making the case for engaging with a social Europe protecting workers' rights. He portrayed the "Leave" campaign as the conspiracy of the rich, offshore elite. And he brushed off problems sometimes attributed to the EU by saying that other EU countries protected their steel industries, and saying: "It is sometimes easier to blame the EU, or worse to blame foreigners, than to face up to our own problems."

The personal touch was limited, but worked well. He said he had had "a few differences with the direction the Labour Party's taken", but was always sure it was "right to stay a member" – "some might say I've even managed to do something about changing that direction". And the final sentence was at last not about why "the Labour Party" had taken a pro-EU position, but, "That is why I am backing Britain in Europe."

He shared the stage with Alan Johnson, head of the Labour In campaign, for questions. Johnson said he was satisfied, and insisted that the power of the convert would have special impact. This performance certainly must have done a little to help the cause of Britain's EU membership.