In Scotland, of course, "independent" has a very different meaning. And this is why the former Labour MPs of The Independent Group, if they take the step of forming a new party to fight the next election across the UK, will struggle north of the border.

It’s telling that the seven MPs all represent English seats. It had been rumoured at one point that Ian Murray, the respected Labour member for Edinburgh South, who is an outspoken critic of Jeremy Corbyn’s leadership, might join them. But, for now at least, he has decided against, saying that while “the current Labour leadership is breaking the broad church that this party once built its electoral success upon … If we work together, our party can be the greatest vehicle for change in this country. It’s the only vehicle.”

It’s not that Labour in Scotland is in better shape than the English party. If anything, it’s in worse — based on seats held, it’s in third place at both Holyrood and Westminster, behind the SNP and the Conservatives. Under its latest leader, Richard Leonard, it has followed Corbyn down the hard-left route (even going further at times) with no polling gains to show.

So a new party’s main obstacle in Scotland wouldn’t be Labour, but the SNP and the Tories. Bumping into a former Tony Blair adviser on a recent trip to London, I was able to say to him “greetings from the land of centrism”. I was only half joking. Scotland went through its radical moment, with swaggering boasts that a left-wing republic was on the way, in 2014. That all looks even sillier in hindsight. The nationalists run a moderate centre-left administration in Edinburgh – Kinnockite, perhaps – with a keen eye on economic growth, while the Tories provide a One Nation – even Blairite - opposition. If UK Labour has veered sharply to the left, and the European Research Group and Brexit is driving the UK Tories to the right, Scotland is sitting this one out.

Those involved in the creation of today’s split know this. One senior figure at the heart of the breakaway says they will need “a different strategy for Scotland”. He admits that in their desire to create a broad new coalition of support they even entertained the idea of asking Ruth Davidson, the popular leader of the Scottish Tories, to lead the new movement. Davidson, who is on maternity leave, doesn’t look favorably on the suggestion.

So that’s the problem The Independent Group faces in Scotland: where’s the space? The matter of national independence aside, choices made up here operate within narrower ideological parameters. The government, for the most part, is more stable. The opposition wants to fight it out on the centre ground. The leaders of both are relatively well-liked and seen as competent. What do Chuka Umunna and friends have to offer that sets them apart in such a context? And if the new movement works, and British politics is saved by a breakaway centrist movement that is wholly English, what does that mean for the future of the Union?

Perhaps the one chink of light in Scotland is the voting system for Holyrood elections. It is a two-tier system which contains an element of proportional representation, which over the past 20 years has allowed smaller parties like the Greens, the Scottish Socialists, and the Senior Citizens Unity Party to win seats. But of these, only the Greens have established an enduring foothold.

There are plenty voters in Scotland who will be cheering the Westminster rebels on, and wishing them every success. There are plenty of Labour and Tory politicians who are scunnered with the behaviour of their Westminster party-mates. But that doesn’t make it any easier to see what a successful, “different strategy for Scotland” might look like.