Little more than five years ago, Labour won 41 Commons seats in Scotland to the SNP’s mere six.  It remained the dominant party north of the border, as it had been for most of the post-war period.  But those MPs were Potemkin Parliamentarians: a display behind which lay…nothing.  No constituency presence to speak of.  No members on the ground to form a constituency presence with.  Why bother with members in rotten boroughs?  Indeed, why bother doing much work in the Commons?  Labour would win in these constituencies because Labour always did.  Then came May last year. “And the rain descended, and the floods came, and the winds blew, and beat upon that house; and it fell: and great was the fall of it.”

The parallel between Labour in its Scottish heartlands and Labour in its English ones is not exact.  The writing was on the wall for Labour in Scotland.  It has a devolved parliament.  England does not.  The SNP had won a Holyrood majority in 2011.  There is no English Parliament and no English SNP: UKIP doesn’t hold a majority on a single local council.  But this EU referendum is exposing a chasm between Labour and its English voters – outside inner London, anyway – that threatens to send its MPs one way and its voters the other.  Polly Toynbee in the Guardian, campaigning for Remain, gives you the flavour: “We had sheets of Labour-supporting names to call in Nottinghamshire – and the results were grim. “Out”, “Out” and “Out” in call after call, only a couple for remain.”

“Here,” she writes, “were the two irreconcilable faces of Labour, eager young London graduates on the phone making scant headway with older traditional voters of Nottingham”.  And what has brought this parting of electoral allies about?  Toynbee doesn’t funk the answer: immigration.

Despite today’s encouraging polls for Leave, Remain must still be favourites to win.  But Brexiteers will be optiministic in one respect at least.  Labour has no answer on immigration that will satisfy its natural core vote.  The messenger may be Gordon Brown, lumbering from his lair to try to save Britain’s EU membership.  It may be Alan Johnson, a ghostly reminder of the one-time electoral sway of the man Brown deposed, Tony Blair.  Or it may be Jeremy Corbyn, the party’s leader, hauled out of his bunker to the same end.  But none has a message that these voters are willing to listen to.  Blairite and Trot, Brownite and Stalinist – all flung open the immigration door when in office, and most still say it should be held open now.

There are exceptions: mostly Labour MPs who realise that the party’s heartland seats are at risk.  Andy Burnham is one.  There is also a distinguished gentleman who has already lost his.  Ed Balls urges readers in today’s Daily Mirror to back Remain.  But his article merely screws tighter the vice in which Labour is already trapped.  “We need to press Europe to restore proper borders, and put new controls on economic migration,” he writes.  But this is not on offer, as he knows perfectly well.  Free movement is an EU fundamental.  To ask for EU membership plus an end to it is like asking a waterfall to flow upwards.  It is a contradiction in terms.  No wonder the smarter Labour MPs, such as Tom Watson, have started talking about something else.

Namely, that a post-Brexit Boris Johnson-led government would slash public services, cut benefits, and so forth.  But there is a deep problem in selling this line – in short, that Labour has already exhausted much of this rhetoric on…real-life pro-Remain Prime Minister David Cameron and real-life pro-Remain Chancellor George Osborne.

Furthermore, Labour’s core constituency isn’t stupid.  It can count.  It knows that even if Boris and Michael Gove intended to do anything of the kind – which they don’t – the Parliamentary arithmetic isn’t there to sustain it.

The Government couldn’t get tax credit reform through the Commons.  Nor a timetable for academisation.  Nor a more liberal Sunday trading regime.  Nor pension change.  If it lacked a majority for any of these, then so too would a post-Brexit government – let alone for wider, deeper change of any kind.

Sidelined by Ruth Davidson in Scotland, exposed by the referendum in England, with no answer to a migration problem which it did so much to create, Labour is hoist with its own petard as it seeks to get out a working-class Remain vote that just isn’t there.