The decision by the European Union to accept Theresa May’s call for an extension of the article 50 period means that for politicians and the public there is a brief and welcome break from Brexit-mania – and a chance to reflect on a route out of our current cul-de-sac. For Labour, this should focus on the electoral impact of the Brexit position we ultimately adopt. The strategy of constructive ambiguity that has allowed the party to look both ways on Brexit since 2016, sustaining a coalition of leave and remain voters, has now run out of road. The pitiless gaze of the public in the forthcoming European elections will melt Labour’s fudge.

For a few Bennite nostalgics, the rationale for this hedging is ideological – an attempt to maintain their fantasy of a leftwing Brexit, or Lexit, in which we’d be free from the EU’s falsely ascribed neoliberalism. But for others, it is rooted in wholly reasonable concerns about how a pro-people’s vote agenda would affect Labour’s vote, especially in constituencies where a majority opted to leave. The claim of MPs such as John Mann in Bassetlaw or Caroline Flint in Don Valley is, in essence, that “working-class” Labour voters would abandon us if we were seen to block the 2016 referendum result, thus denying Labour power for generations to come.

It is a powerful, emotional argument, of course, especially in a party born out of the working class. But it is not an argument supported by engagement with the facts. The facts are quite clear and have been repeatedly reinforced by polling evidence and analysis, most recently in the work of Christina Pagel and Christabel Cooper in research funded by University College London. Their polling of over 5,000 people shows that, on average, about two-thirds of Labour voters across the UK voted remain in 2016, ranging from 74% in London to 66% in Scotland and 59% in the Midlands.

Those majorities are big enough for the psephologists to agree that, in practically every current Labour seat, most of our voters voted remain. Meaning that the biggest threat we face in retaining support is losing remain voters disillusioned by our prevarication on a people’s vote. That fact also applies to the 80 seats that Labour has to win at the next election if we are to form a majority. Arguably, more so, as almost half of those target seats voted remain overall in 2016, whereas 60% of the seats we hold voted leave.

The UCL analysis shows that in every region of the UK, the majority of voters who put a cross next to Labour in the general election of 2017 but say they won’t vote Labour next time, are switching to a party they see as more pro-European. In London, where Labour dominated in 2017, a third of Labour voters who know how they intend to vote now say they will vote for another party, but voters switching to a party seen as more pro-remain outnumber those switching to a more pro-leave party by five to one. In the north of England, the number switching is fewer, at just 20% – but again the number switching to a more pro-remain party outnumber those switching to the Tories or Ukip by four to one.

In the Midlands, where a quarter of Labour voters say they are switching, remainers outnumber leavers by five to one. Starkest of all is Scotland, where Labour must win 23 of those 80 seats to form a government. There, 48% of our 2017 voters now say they plan to defect, 45% to a more pro-remain party, just 3% the other way – a ratio of 15 to one.

But will moving towards a people’s vote and remain alienate Labour’s leave voters? Pagel and Cooper’s work shows that Labour leave voters are much more likely to have changed their minds on Brexit than any other voters. By contrast, our remain voter base are barely changing their minds at all. Of Labour’s 2017 support who voted to leave, the UCL analysis shows 18% have now shifted to remain. That stands in stark contrast to the position among Tory voters, of whom just 4% have switched from leave to remain, against 28% of Tory remainers who now want the hardest of Brexits.

The study suggests that finances are the reason for this change of heart among almost a fifth of Labour’s leave voters. Struggling leave voters who voted Labour in 2017 fear the financial consequences of Brexit. Labour has far more to lose by equivocating on Brexit than we have to gain by “respecting the referendum”.

One of the few truisms to emerge from the Brexit saga is that there are no perfect political choices to be made by either party. The Conservative party is split between 44% at one end of the spectrum, who want to cleave the waters of the English Channel with the hardest of Brexits, and 20% at the other, who still want to remain. For Labour, however, the numbers should stiffen the resolve of our leadership to take a clearer position; pro-people’s vote and remain. The numbers should also give succour to those who fear Labour leave-voter support is hardening against us, especially in constituencies that voted overall to leave.

For us, there clearly are some choices that are better in terms of electoral self-interest. At the last election, we put off making those choices, seeking to look both ways on Brexit, and to some extent, it worked, with 8 million remain voters and 4 million leavers putting their cross next to Labour. But that coalition could not be sustained through a European poll, another six months of Brexit chaos and into the general election that surely must come before the year is out. The time has come for Labour to decide which way to face.

Many Labour men and women believe that our values should always have made that an obvious choice, but electoral calculus always plays a part in political decision-making. Fear that Labour will lose the next election if it stands firm for a people’s vote and a chance for voters to reassess has clearly played a part in our prevarication. But the numbers don’t lie. Labour has much more to lose than we might win by acquiescing in Brexit, or worse, enabling it. We are a remain party in our hearts and in our heartlands and the route to winning the next election is to be true to both and support the people’s right to change their mind.

• Owen Smith is Labour MP for Pontypridd