Having spent the first part of the campaign seeing the pro-Remain message they badly need voters to hear – that Brexit represents a risk the NHS can’t afford to take, that a Leave vote would trigger further austerity – drowned out by Conservative in-fighting, Britain Stronger In Europe might decide, as David Lloyd George once quipped, that “a change of nuisance is as good as holiday”.

Or they might feel a pang of frustration that the message is now being overshadowed by red-on-red attacks.

The cause of the row is free movement. Tom Watson, Labour’s deputy leader, has said that Labour should back a Remain vote in order to “re-negotiate” the free movement of people in the European Union, and he’s been backed up by Yvette Cooper and Ed Balls.

Jeremy Corbyn has hit back, telling BuzzFeed that he will never support changes to free movement. Michael Dugher has responded in kind on Twitter, suggesting that Corbyn wants to lose the referendum.

For Labour, politics are fraught, externally and internally. The issue of border control, as I wrote on Monday, splits Labour’s core vote – the socially concerned and the poor – in two. Labour cannot even get close to winning an election without both groups. The party’s political problem has now taken on historical significance as Labour voters who are worried about immigration are backing Brexit, putting Britain’s membership of the European Union on the brink.

As far as the external politics are concerned, I wrote on Labour’s migration dilemma on Monday and I don’t wish to go over old ground, so I’ll be brief: bluntly no British government is going to be able to renegotiate the Treaty of Rome and the free movement of people. (Not least because the governments of Poland, Lithuania, Spain and other countries with large flows of migrants to Britain will never accept having to go to their own voters at election time having made it harder for them to come to Britain to work.) If Labour is for staying in the European Union then it needs to find a way to win an election on a pro-immigration platform. It’s really that simple.

The internal politics are more interesting. Readers with long memories will note that all of the politicians calling for curbs on free movement – Dugher, Cooper, Watson and of course Balls himself – were supporters of Ed Balls’ leadership campaign in 2010. Crucially, they formed one half of the “Brownite split” over immigration that plagued the Ed Miliband years.

Douglas Alexander was the most senior politician on the other pole. He formed an alliance with Chuka Umunna at shadow BIS to block Labour from going into the election supporting a referendum (it feels relevant at this point to note that this was because Alexander believed that Labour was not in the right shape to win a referendum after decades of built-up anti-immigration sentiment).

That row took on a particularly acrid nature after Ukip won the 2014 European elections and Labour finished a poor second. The result, as so often under Miliband, was muddled compromise: Umunna and Alexander got the commitment not to hold a referendum, something further bolstered with the appointment of Pat McFadden to the frontbench in October 2014. The Balls-Cooper connection got Miliband’s promise to “bear down” on immigration and the “controls on immigration” pledge with accompanying crockery.

But as interesting as Labour’s internal splits are, as far as the Remain campaign is concerned the politics are not fraught at all. Stronger In’s polling is crystal clear: what Labour and the rest of the pro-Remain forces need to do is increase the salience of the economic costs of quitting the single market, in the words of one senior source, “remind Labour voters they have the most to lose from a recession”. That approach is furthered supported by a public poll by ComRes for today’s Sun showing that 68 per cent of voters would be unwilling to bear any financial hit to reduce immigration – Cooper and co are “re-litigating” the 2014-5 rows over immigration.

That’s the approach that Labour and the rest of the Remain campaign need to take over the next eight days, rather than promising to unpick the central tenets of EU membership.