Last week, YouGov published the results of a poll that ought to set nerves jangling throughout the Labour Party. It showed support for the Conservative Party among C2, D and E voters at 48 per cent, compared to Labour at 35 per cent. These figures compare very sharply with those from an identical poll in January this year, which showed almost exactly the reverse position, with support for Labour among the same groups of voters at 46 per cent and for the Conservatives at 37 per cent.

One poll is not necessarily decisive and what counts is election results, not what the polls say. All the same, the scale of the change in support that these figures suggest is highly alarming. What could have gone wrong to produce this sort of appalling result, especially at a time when the Tory government is evidently undergoing major difficulties – and indeed more clearly divided in parliament, particularly over Brexit, than the Labour Party?

The answer is almost certainly related to Brexit. Leaving the EU has been the dominant political story for the last six months. It is therefore hard to believe that the dramatic fall in support for Labour among many of our erstwhile core voters has nothing to do with what Labour has been doing – both in the Lords and the House of Commons – to undermine the result of the 2016 EU referendum. By fomenting wrecking amendments to the Withdrawal Bill in the House of Lords and by supporting the UK staying in “a” or more probably “the” EU customs union in the House of Commons, traditional Labour voters – large numbers of whom chose Leave – can see what many of them voted for in the referendum being eroded.

Labour is now so dominated by its young, metropolitan, internationalist and pro-EU supporters that it is in grave danger of forgetting that to win elections, it has to do much more than mobilise its middle-class adherents. It also needs to bring with it its traditional working-class support. If it fails to do so, parliamentary tactics on Brexit could well turn out to be counter-productive. Those strategies, which are at least partly orientated not towards a national effort to secure a reasonable outcome to Brexit but to bringing down the government, are useless should the support Labour needs to win the next general election melt away.

The pattern of voting during the referendum shows how fragile Labour’s position is. Of all the seats held by Labour at the time of the referendum, almost 70 per cent had Leave majorities. Many traditional Labour voters in these seats supported Labour in the 2017 general election because the party, in its manifesto, promised to accept the referendum result and to make Brexit a reality. These voters can see as clearly as anyone else that the drift towards a softer and softer Brexit, which Labour now appears to support, is not going to deliver the sort of outcome Leavers voted for.

If we finish up still paying large sums of money every year into the EU coffers, still not in control of our borders, under the legislative control of the European Court of Justice, still stuck in the Common Agricultural and Common Fisheries Policies and unable to arrange our own trade deals, even if nominally we have left the EU, we will clearly still be mostly in it – with no say about how it develops.

Labour therefore needs to think very carefully where it is going. The surge of new members, many of whom are Remainers, has its benefits. But if the result is a haemorrhaging of support among our traditional voters, we will be no closer to a Labour government than before.

John Mills is the founder of consumer goods giant JML and has been a major Labour donor. He chairs Labour Leave and Labour Future.