Ahead of today’s meeting of Labour’s shadow cabinet, here is a thought experiment. In the latest YouGov poll, the party has lost half its vote at the last general election. Suppose three-quarters of those lost voters had switched to the Brexit parties or the Conservatives, while one-quarter had switched to strongly remain parties – the Liberal Democrats, Greens or SNP. Pro-leave MPs in Labour’s heartlands would say “told you”. The case for Labour pivoting to a strongly pro-leave stance would be overwhelming.

The laudable aim of healing divisions cannot succeed while the issue of Brexit remains unresolved

In fact the opposite is true. Of those who voted Labour in 2017, just 51% would vote Labour today. Thirty-six per cent would vote Lib Dem, Green or SNP; just 11% would vote for the Brexit party or (in a very few cases) Conservative. If any pivoting is needed, the direction needed for the party’s self-preservation is clear.

More importantly, though last month’s European parliament elections have shaken the political kaleidoscope, the underlying trends have been clear for months. The swing in national opinion from 52% to 48% in favour of leave in 2016 to 44% to 56% in favour of remain, if we take an average of recent polls, has been driven by two main factors. The first is demographic (older, mainly leave, voters dying while overwhelmingly pro-remain teenagers reaching voting age). The second is Labour voters changing their minds – especially in the party’s northern and midlands heartlands. One particular group that has swung decisively to remain are Britain’s nurses. Many of them were persuaded by the promise of an extra £350m a week for the NHS, and they now feel they were deceived.

These trends have been visible for months. Like ripe apples in the autumn, many Labour supporters, uneasy about the party’s equivocal stance on Brexit and a new referendum, were ready to drop from the tree. Last month’s election provided the gust of wind to detach them. And every poll in the four weeks since the election has found that most of them have stayed on the ground.

It is plainly true that a decisive move towards a fresh referendum would risk the loss of some strongly pro-leave Labour votes. But the numbers are small. (In all bar a very few constituencies, most Labour supporters in leave constituencies voted remain three years ago: it was non-Labour supporters that supplied the leave majorities in Sunderland and elsewhere.)

The far larger numbers, in 2016 and even more so today, are people who voted in 2017 for Jeremy Corbyn to become prime minister and today want the UK to stay in the EU. The consistent signs from the polls since last summer, and from last month’s election, are that voters are increasingly polarised on Brexit.

Labour’s attempt to straddle the remain-leave divide was defensible as a means to bring together a divided nation. However, it was electorally disastrous. It has become clear that the laudable aim of healing those divisions cannot succeed while the issue of Brexit remains unresolved. The immediate electoral, and arguably moral, challenge for Labour – and, for that matter, politicians in all parties – is to work for a decisive outcome to the current crisis. National harmony is an ambition for tomorrow and not, sadly, today.

• Peter Kellner is former president of YouGov