Nicola Sturgeon has promised to exhaust all options in an effort to keep Scotland in the EU after the country voted by 62 per cent to 38 per cent against Brexit.

But few people hold out much hope for her diplomatic charm offensive in Brussels' corridors of power.

The First Minister herself has said a second independence referendum is "highly likely" as the only means of avoiding Scexit, and her supporters are in no doubt about the direction of constitutional travel. Kezia Dugdale, the Scottish Labour leader, was derided by online Nationalists on Thursday when she declared her party was the only one committed to keeping Scotland in both the EU and the UK. Independence supporters dismissed the notion as a laughable impossibility.

They might well be right. Ms Dugdale's hopes rest on what she herself described as a "tentative" proposal to reshape the UK as a federal state.

Details are sketchy but, speaking after making a speech on the consequences of Brexit in Edinburgh, she confirmed that former Labour lord chancellor Lord Falconer was investigating whether moving to a federal set-up would allow the UK's devolved nations, and even English city regions, to negotiate their own membership of the EU while remaining part of the Union. If so, not only Scotland but Northern Ireland (which voted 56 per cent to 44 per cent to remain) and perhaps London (60-40 in favour of staying in the EU) could strike their own deals with Brussels.

It sounds far fetched. Even if the other EU member states were amenable to the idea, the UK would have to wrestle with the fraught question of having different national and regional arrangements for trade and freedom of movement.

Let's assume for a moment they could be resolved. It would still be stretching credulity to think they could be resolved quickly. Creating such a system would surely take as long or longer than Britain's looming Brexit talks.

My hunch is that a federal UK will not provide Labour with a clear-cut route to keeping Scotland in the EU and the UK and certainly not before Ms Sturgeon has called a second independence referendum.

In fairness, Ms Dugdale appears equally realistic. "I don't know what the answer is," she admitted when she faced questions after her speech this week.

Interestingly, though, Labour are not the only people considering a federal future for the UK.

Murdo Fraser, the free-thinking Conservative MSP who called for the Scots Tories to split from the UK party during his unsuccessful leadership bid five years ago, has thrown his weight behind the idea in a blog for the Reform Scotland think tank.

It is a typically thoughtful piece of work that touches on the long history of federalism in Britain and looks at it use in other countries before considering how it might work in Britain.

In Mr Fraser's vision, federalism could be achieved "without the perception of a great deal of change" for people living in Scotland and the UK's other devolved nations.

The role of Holyrood would be enshrined in a written UK constitution but, apart from the that, the parliament's imminent new powers over tax and welfare would go a long way towards to completing the Scottish part of the federal jigsaw puzzle.

England would require a de facto English parliament and city regions like Manchester significantly greater powers. The House of Lords would be replaced by a Senate providing equal representation for the federated parts of the UK.

The system would allow for fiscal transfers, allowing wealthier areas to support poorer ones and, argues the MSP, it could all be brought into being relatively painlessly.

Mr Fraser accepts the 2014 referendum split Scotland down the middle and says starkly: "It is hard to see that the

UK is sustainable in an unreformed state if 45 per cent of the population of one component part wish to leave".

The solution, he believes, should appeal to Unionists and might even satisfy a good many Yes voters.

Whether you agree or disagree, this is a welcome contribution to the debate about Scotland's constitutional future.

What Mr Fraser does not do, however, is link federalism to Scotland's continued membership of the EU. The plan is intended as an alternative to independence, not a means of thwarting Brexit. Which prompts this thought: if we are to have another referendum, might federalism be the new Vow?