JEREMY Corbyn and Owen Smith came to Scotland last week to reject the idea of a progressive alliance with the SNP. They left with Labour looking as if it can scarcely establish a progressive alliance with itself.

At the hustings debate in Glasgow, Smith accused the Labour leader of being a closet Brexiteer and questioned whether he had even voted Remain in the EU referendum. We've become used to these personal attacks in Labour's civil war, but it was still astonishing to see divisions laid so brutally bare in a public forum. How can these people hope to remain in the same party after Jeremy Corbyn wins next month, as everyone expects he will?

The former Labour special adviser, Paul Sinclair, says that it is the Scottish Labour Party that will split first. He forecast on BBC Scotland that the deputy leader of Scottish Labour, Alex Rowley – “a man whose ambition is in inverse proportion to his abilities” – would challenge Kezia Dugdale on the morning after a Corbyn victory.

There certainly seemed no love lost, evidenced by the chorus of boos from some Labour supporters when Kezia Dugdale's very name was mentioned in the hustings. Imagine Nicola Sturgeon being booed at an SNP rally. But is there room for two Labour parties in Scotland? They only have one MP in Westminster, the Edinburgh member, Ian Murray. Would they split him in two, or have a time-share? The party has already lost its position as the main opposition in Holyrood. If Scottish Labour split, the remnants might end up vying with the Liberal Democrats and the Greens for fourth place.

Hitherto, few have considered a Scottish split a serious possibility, but it actually does make some kind of sense. The fundamental divide in the Scottish Labour Party right now is between those who want a wholly autonomous organisation, like Mr Rowley, and those, like Kezia Dugdale, who want the party to remain essentially a “branch office” (copyright Johann Lamont 2014), albeit a thoroughly devolved one.

This divide mirrors the constitutional divide in Scotland between independence and those who want to remain in the Union. It is hardly surprising that this divide should manifest itself also in the Labour Party. That it has overlapped with the division over the UK leader, Smith or Corbyn, is not too surprising either. Those who want an independent Scottish Labour Party would tend to be of the left and more likely to oppose Owen Smith, who seems to represent continuity with Tony Blair, whose unpopularity is seen by many on the left as the proximate cause of the SNP's rise.

Of course, both sides of Labour are united on one thing: hatred of the Scottish National Party. Both Corbyn and Smith insisted last week that under no circumstances would they form a progressive alliance with the SNP after the next general election. This tribalism is to be expected, but it is depressing for voters looking to Labour to lead a viable alternative to the Tories in Westminster. Neal Lawson, leader of the pro-Labour Compass think tank, said it was "ridiculous" to rule out co-operation: “The electoral arithmetic demands a progressive alliance,” he said.

The political reality is that a Labour leader would have to speak to the SNP if they wanted to become Prime Minister. Even assuming Labour recovers before the next general election it is almost inconceivable that it would be able to govern on its own, whoever is leading it. It would be daft not to invite the 56 Nationalist MPs to support a Labour administration that would lock the Conservatives out of government. It needn't be a formal coalition, just a confidence and supply arrangement.

The rejection of a progressive alliance might be understandable if there were significant policy differences between the SNP and Labour, but there aren't any more. The policies being promoted by both Corbyn and Owen Smith are remarkably similar to those in the SNP’s 2015 general election manifesto: 50p tax band, mansion tax, mass house building and so on. Nicola Sturgeon was attacked in May 2015 by Labour as irresponsible for calling for a £180bn UK-wide infrastructure programme financed by additional borrowing of 0.5 per cent a year. Now both Smith and Corbyn are offering levels of borrowing even higher than Sturgeon’s: Smith promised £200bn last week for roads, housing and health, while Corbyn has proposed £500bn to be disbursed by a network of national investment banks.

And even without an election, the case for co-operation between Labour and the SNP in Westminster becomes stronger by the day. Whoever wins the Labour leadership will surely join with Nicola Sturgeon in opposing the abolition of the Human Rights Act, which the new PM, Theresa May, has put back on the table. Labour and the SNP were able to defeat the abolition of tax credits by George Osborne – with a little help from the House of Lords – and they will surely be challenging Universal Credit.

Then there is Europe. Corbyn and Smith disagree on the idea of a repeat referendum on EU membership, but surely they will both be pushing in Westminster for “soft Brexit” – in other words, for Britain to remain within the European Economic Area which encompasses the single European market and free movement. That is also Nicola Sturgeon’s number one priority, should she decide not to hold a referendum on independence. Given the confusion in the UK Government about what Brexit means, it should be entirely possible for the Westminster parties to block a “hard” Brexit – but only if they work together.

As Unionists, the UK Labour leadership contenders could not be expected to support an independence referendum for Scotland. But the way things are going in the party north of the Border, Labour may find that it is forced to be open-minded about that too, as Kezia Dugdale herself has been. In April she suggested that she might be prepared to vote Yes to independence if there was a vote in the UK to leave the EU. She has since retracted, but there is no doubt that many in the party are now in two minds about independence. I fully expect that, if there is another independence referendum, Labour will allow its members the freedom in Scotland to campaign for both sides. The Labour victor in the Fife Lochs council by-election last week, Mary Lockhart, for example, is a supporter of independence.

But that's if the Scottish Labour Party is still a going concern and that clearly is in doubt. The enmity that is being generated by this leadership election is now out of control. Labour Party figures are openly abusing each other on social media in a manner that is unprecedented. Not since the days of Michael Foot and Tony Benn in the 1980s has there been such recrimination, though in many ways it is much worse today. Most Labour MPs in Westminster have delivered a vote of no confidence in their leader, which never happened to Michael Foot.

Few thought that the crisis in the Scottish party could get any worse after the Tsunami election in which they lost all but one of their 41 MPs. It just did.