When the campaign to keep Britain in the EU ran focus groups, it found that many people do not know what the single market is. Perhaps some thought it was a club where one singleton could pick up another, rather than the largest tariff-free trade club in the world.

It was a reality check but all was not lost: surprisingly, the group discussions showed that people knew about and liked the European arrest warrant, raising the In camp’s hopes that national security could be a vote-winner in the referendum.

Pro-Europeans know they have a huge explaining job to do before the referendum – not least because those who want to leave the EU will be much more likely to turn out. Differential turnout could be crucial in a tight race, and I suspect it will be close.

Some Europhiles worry that, despite the Labour’s official support for the In campaign, Jeremy Corbyn is lukewarm. Alarm bells started to ring after the Labour leader told David Cameron in the Commons on Wednesday he was “negotiating the wrong goals in the wrong way for the wrong reasons.” He said the Prime Minister’s much-trumpeted reforms were “simply tinkering around the edges. They have little impact on what the EU delivers for workers in Britain or British businesses.” Mr Corbyn hardly sounded like a cheerleader for the In crowd.

He was right to describe the renegotiation as “a Tory Party drama that is being played out in front of us.” The clamour for a referendum came from the Conservative family rather than the country. The only questions to Mr Cameron that mattered after his Commons statement on the new deal were from Conservative MPs. “I thought I had stumbled into the weekly meeting of the 1922 Committee [of Tory MPs],” one Labour MP quipped afterwards.

Some Labour MPs are frustrated that they cannot exploit the glaring Tory divisions on an issue on which Labour is broadly united. And it is the duty of all Opposition leaders to…well, oppose. We can hardly expect a left-wing Labour leader to be an echo chamber for a Tory Prime Minister with whom he has so little in common. Although they agree in principle on Europe, they will not share a platform. It would be impossible to run a “command and control” In campaign with all parties singing from the same hymn sheet. Better Together tried it in the Scottish referendum, creating a cumbersome campaign in which everything had to be signed off by all the political parties opposing independence.

Britain Stronger in Europe (always called “BSE” by the Outers) will make a virtue out of the pro-EU parties doing their own thing and sending different messages to different audiences. But will Mr Corbyn really make an effort to reach the parts that Mr Cameron cannot reach? Some Labour Europhiles doubt it.

Mr Corbyn has form. He voted against EU membership in the 1975 referendum. Many in the labour movement were converted to the EU cause by Jacques Delors, then European Commission President, at the 1988 TUC conference. His landmark speech persuaded many that the EU could improve workers’ rights rather than be a capitalist club trying to erode them. Hilary Benn, the shadow Foreign Secretary, who voted to leave in 1975, was won over but his late father Tony, spiritual leader of the British left, was not. He regarded the EU as an attempt to build an anti-democratic empire. Mr Corbyn, a disciple of Tony, was with him rather than Hilary.

It showed during last year’s Labour leadership campaign when at one point Mr Corbyn refused to rule out Labour advocating an Out vote in the referendum. But after winning the leadership, Mr Corbyn bowed to the inevitable: an estimated 211 of Labour’s 232 MPs support EU membership. Hilary Benn was reassured that Labour would still support the In camp. There was no great row. Mr Corbyn had more important fish to fry –notably, persuading Labour to change tack and oppose the Trident nuclear weapons system.

Labour Europhiles worry that Mr Corbyn’s instincts will hold back the In campaign. “He doesn’t like the West or its institutions –like the EU or NATO,” one MP groaned. “He is not really an internationalist, despite the obvious merit of tackling issues like climate change at EU level.”

However, not all Labour MPs are fully paid up Europhiles. Some are haunted by the cross-party referendum campaign in Scotland, after which Labour lost 40 of its 41 Scottish seats at last year’s general election. But it is a false analogy: the Tories were hated in Scotland, but are not in England.

Other Labour MPs worry about the threat from Ukip, which took more votes from Labour than the party expected last year and is now in second place behind Labour in 34 northern constituencies.

Corbyn allies point out that he went to Brussels in December for positive talks with Labour’s sister parties when he did not have to. Yet some Europhiles fear the referendum could be lost unless the Labour leader puts his shoulder to the wheel. “The public know that Cameron and Corbyn don’t agree, so seeing them both making the case for Europe would be powerful,” said one In campaigner.