Two by-elections next week in historically safe Labour seats are generating more than the usual level of interest for such contests. The principal opposition party rarely loses a seat it is defending in a by-election – it has only happened four times since 1979. Yet it is being seriously suggested that the Labour party could lose Copeland to the Conservatives, and, perhaps more importantly, Stoke Central to UKIP, where the party’s new leader, Paul Nuttall, is its nominee.

Not least of the reasons for this speculation is Labour’s dire position in the opinion polls. The most recent polls from each of ComRes, ICM, Ipsos MORI, Opinium and YouGov on average credit the party with just 27% of the vote; it has not hitherto been that low in the polls since the 1983 UK general election. Rarely has an opposition party looked as vulnerable in the mid-term of a parliament as Labour does now.

But there is also another reason for the interest – the observation, courtesy of Chris Hanretty, that in nearly two-thirds of the seats held by the party (and in no less than four-fifths of those located in the North of England and the Midlands) a majority of voters voted to leave the EU.

Cue much discussion about the party’s need to ‘reconnect’ with traditional, working class Labour voters in the party’s provincial heartlands, many of whom supposedly voted to Leave, and thus fend off the threat to that vote from UKIP – a threat for which the Stoke by-election in particular is being portrayed as a litmus test. It has even been suggested that unless it does so, the party might find that the EU referendum does as much damage to its electoral prospects in North of England as the independence referendum has done in Scotland.

Analysis of election and referendum outcomes by constituency can be highly informative – I do a fair amount of it myself. But it always needs to be interpreted with care. In particular, it does not necessarily follow that because a majority of all voters in most Labour constituencies voted to Leave, most Labour voters in those constituencies must have voted that way. After all, there are plenty of people who did not vote Labour in those seats.

On average the party won just half the vote – and less than a third of the electorate – in them in 2015. So there are plenty of non-Labour voters whose choice last June could also have been responsible for the overall pro-Leave outcome in Labour held seats.

To ascertain how individual Labour voters (as opposed to all voters in Labour-held constituencies) behaved in the referendum we have to look to the evidence of surveys that have asked voters how they voted. The largest survey of how people voted in the referendum is an internet panel run by the academic British Election Study (BES). It interviewed just over 30,000 people after the referendum, and thus is big enough not only to look at how Labour voters behaved across the country as a whole, but also in particular parts, such as in the North of England or in Labour-held seats.

First up, according to this survey across Britain as a whole, 63% of those who voted Labour in 2015 and who cast a ballot in the EU referendum last June voted to Remain. This estimate is not dissimilar to that of other surveys. NatCen’s internet panel also put the figure at 63% when it asked people last September how they had voted, while YouGov’s on the day poll put the figure at 65% and Lord Ashcroft’s similar exercise reckoned it was just a little higher at 70%. So there is no doubt that across Britain as a whole, most Labour voters – probably nearly two in three – voted to Remain.

But is this true everywhere? After all, according to Hanretty’s estimates, in Labour-held seats in London and the South of England on average 61% voted for Remain, whereas in the North of England and the Midlands only 42% did so. Perhaps in the more ‘traditional’ Labour territory in the North of England and the Midlands, most Labour voters did in fact back Leave?

Not so, according to the BES data. True, as the table shows, Labour voters in the North of England and the Midlands were less likely to vote for Remain than their counterparts elsewhere in the UK. However, it is still the case that a clear majority of Labour voters across these two regions (58%) voted to Remain. Moreover, Labour were by no means unique in having a more Eurosceptic body of supporters in the North and the Midlands – those who voted for other parties in the northern half of England, including for the Conservatives, were also somewhat less likely to vote for Remain than their counterparts elsewhere.

In short, the higher level of support for Leave in the North and the Midlands is not just accounted for by the behaviour of Labour voters there. Indeed, but for the behaviour of those who did not vote Labour, those two parts of England would have recorded a majority vote to Remain.

But, you may ask, what about the position in those seats that Labour actually won in 2015? Is it not this that matters? In fact, the answer proves to be much the same. According to the BES, in Labour-held seats across Britain as a whole 63% of Labour voters voted to Remain, exactly the same as the proportion across the country as a whole. As we might now expect, the figure is somewhat lower in Labour seats located in the North of England and the Midlands, but at 57% it is not significantly different from the proportion (58%) across the North of England and the Midlands as a whole.

So, a substantial minority of 2015 Labour voters in Labour-held seats in the North of England and the Midlands did vote to Leave. But it is no more than a minority. Indeed, it is not much bigger than the proportion of Conservative voters in Conservative-held seats who voted for Remain (37%), a group whose continued loyalty to their party might also be thought to be potentially vulnerable in the wake of the Brexit vote.

Ensuring Labour’s survival in the North of England and the Midlands is not just a question of strengthening the party’s appeal to the so-called traditional Labour voter who voted to Leave. There are simply not enough of them for that alone to be a viable strategy. Rather, it is also about retaining the support of the majority of Labour voters in the northern half of England who voted to Remain. For without them, the party really will be in trouble.

By John Curtice, senior fellow at The UK in a Changing Europe and Professor of Politics at Strathclyde University. This posted originally featured on WhatUKthinksEU.