The Labour party was already having enough difficulty keeping itself together without a referendum on Britain’s membership of the European Union coming along. The party was reeling from the election of a leader who was not only well to the left of most of his parliamentary colleagues but also did not obviously have the personal skills needed to do the job. However, the referendum on the EU has compounded the party’s difficulties by exposing another fissure – between its traditional white working-class supporters and its public-sector socially liberal middle-class ones (including the vast bulk of its parliamentary party). In combination, these two divisions threaten to tear the party apart.

Elections in the UK are usually about the left and right of politics, whether the government should do a little more or a little less. On this, Labour’s working- and middle-class supporters tend to be at one: they all, albeit to varying degrees, want the state to do more, to curb the excesses of the capitalist market, and to produce more equitable outcomes. So long as the political conflict focuses on this set of calculations then they are a viable electoral coalition.

However, the EU referendum was not about the size and the role of the British state. It was about what Britain’s relationship should be with an intergovernmental organisation that epitomises one of the major social and economic phenomena of our time: globalisation. This phenomenon has had significant economic and cultural consequences, including (not least) substantial flows of migrants in search of work in an internationalised labour market.

Among young university graduates this development is regarded as an opportunity rather than a threat. After all, this is the world in which they have grown up. They have acquired the skills required to compete in the global market place. Indeed, many will become migrants themselves, deploying their valued skills in Berlin or Barcelona. Meanwhile the experience of university, in which international students are often commonplace, has led them to embrace the cultural diversity that immigration brings.

This world looks very different to many an older white working-class voter who left school at the earliest opportunity. They are used to a world in which everyone speaks the same language and shares a common set of cultural values and mores. In this light, then, the relatively high levels of immigration that the UK has experienced in recent years is regarded as a threat. They want back the country in which they grew up and in which they once felt comfortable. Meanwhile, many suspect that the inflow of migrants helps to explain why they have seen little (if any) increase in their own living standards.

In short, with questions of immigration and identity at its core, the referendum on Britain’s membership of the EU inevitably cut across Labour’s electoral coalition. Indeed, education and age have long been the demographic bases of division between social liberals and social conservatives.

Those with different educational experiences voted very differently. According to a large poll conducted on polling day by Lord Ashcroft, graduates and those still in education voted in favour of remaining in the EU by 59 per cent to 41 per cent, while those whose educational experience did not extend beyond secondary school voted by 65:35 to Leave. Similarly, in their on-the-day exercise, YouGov found that graduates voted 68:32 in favour of Remain, while those whose highest qualification is a GCSE or its equivalent voted by 70:30 to Leave. The party’s middle-class supporters were in a very different place on this issue to their more working-class ones.

Just to compound Labour’s difficulties, there was a clear ethnic division too. Those from an ethnic minority background, who have never shown much inclination to back Ukip, seemingly found the Leave side’s emphasis on reducing immigration relatively unattractive. Lord Ashcroft estimates that only 32 per cent of those from an ethnic minority background voted to Leave, compared with 53 per cent of those who regard themselves as ‘white’. Consequently, another part of Labour’s electoral coalition – Britain’s ethnic minority population – was also on the other side of the referendum divide from the party’s traditional white working-class base.

Against this backdrop it was, in truth, hardly surprising that the highest level of support for Leave was in predominantly working-class local authority areas in the north and midlands of England, where Labour tends to be relatively strong. In the 2014 European parliament elections, Labour won on average 28 per cent of the vote in those local authority areas where less than 22 per cent have a degree, whereas the party won just 20 per cent in areas where more than 32 per cent are graduates. Now, in the referendum, on average Leave won as much as 64 per cent of the vote in those places that fall into the former group, but as little as 42 per cent in the latter. At the same time, no less than 71 of the 90 local authority areas in England and Wales with the fewest graduates are located in the north of England and the Midlands, compared with just 13 of the 83 areas with the most graduates.

In short, the principal explanation for the fact that Leave did so well in the West Midlands (59 per cent), the East Midlands (59 per cent), the North East (58 per cent), and in Yorkshire and the Humber (58 per cent) in particular lies in the demography of Leave support and of those regions, rather than in any particular failings by the Labour party. Indeed, once we have taken the demographic character of an area into account, if anything Remain tended to do rather better the stronger Labour was locally. For example, among those council areas in England and Wales with relatively few graduates, Leave won an average of 62 per cent of the vote in places where Labour won over 25 per cent of the vote in 2014, compared with 67 per cent where Labour won less than 15 per cent two years ago.

Meanwhile, it was, of course, the other parts of the Labour party’s coalition – the socially liberal middle class and the country’s ethnic minority population – that ensured London was the one part of England and Wales that did vote decisively in favour of remaining (by 60 per cent to 40 per cent). No less than 24 of the 33 council areas in the capital have a population in which over 32 per cent are graduates, while 27 of the 41 most ethnically diverse parts of England and Wales are located in the capital. Again, demography was crucial.

Against this backdrop it was hardly surprising that across Britain as a whole only around two-thirds (63 per cent according to Lord Ashcroft, 65 per cent as estimated by YouGov) of those who voted Labour in 2015 voted to remain in the EU. The party was never likely to achieve much more than this. And at least the party’s coalition did not fracture as badly as the one that backed David Cameron a year ago; well under half (42 per cent according to Lord Ashcroft, 39 per cent per YouGov) of those who voted Conservative in 2015 voted to remain. The real source of the Remain side’s difficulties was Cameron’s failure to bring his own voters on board.

Yet it is Jeremy Corbyn who has taken much of the blame inside the Labour party for the Remain side’s failure, as the party’s pre-existing division about his leadership has interacted with the divisions made manifest by the referendum. Of course, MPs are entitled to have made their own judgment about Corbyn’s capabilities for the job, a judgment that his performance in the referendum appears to have reinforced, and upon which they may have felt it had become more pressing to act, given that the outcome of the referendum makes an early general election more likely. But in truth there is little in the pattern of the results of the referendum to suggest that Corbyn was personally responsible for Remain’s defeat. The referendum outcome looks more like a pretext for an attempt to secure Corbyn’s removal than a reason.

However, the referendum does raise questions for all wings of the Labour party, and for its parliamentary party – in which middle-class graduates predominate – above all. As we have argued before, unless the party can persuade the less well-off in Britain that social democracy can tame the tiger of globalised capitalism so that their interests and concerns – cultural as well as economic – can be met, it is at risk of losing their support. We have already seem in Scotland how the politics of identity can cause much of Labour’s working-class support to melt away, and, should Ukip be able to sustain a post-referendum purpose and appeal, there is a risk that a similar politics could have the same effect in England.

Certainly, there was little in the Remain side’s case – as espoused by Labour as well as the Conservatives – that met those concerns. There was, in truth, no answer on how to deal with immigration, while there was little attempt to explain how the UK’s membership of the EU could be used to advance the economic interests of the less well-off. Instead, the only reason offered for voting to remain was the allegedly deleterious consequences of leaving. Telling working-class people that they have to put up with the consequences of globalisation is simply not good enough. Labour needs to take note – whoever leads it.

John Curtice is professor of politics at Strathclyde University and a columnist for Juncture.

This article appears in edition 23.1 of Juncture, IPPR's quarterly journal of politics and ideas, published by Wiley.