Just before the EU referendum, Gordon Brown a released a video urging voters to choose Remain. It was filmed in the ruins of Coventry Cathedral. His message about “leading” Europe not “leaving” it was a social media hit.

In a slightly more sombre speech responding to Brexit today, the former Labour Prime Minister said he had wanted to film the message at the White Cliffs of Dover – which he sees as a symbol of “outward-looking” Britain, a “highway into the world”.

But those very same gleaming cliffs have come to represent the UK’s closed door to the rest of the world. In 2015, Nigel Farage unleashed Ukip’s controversial election campaign poster – depicting escalators to transport migrants up the cliffs – at the same location.

It’s this divide that Brown was decrying as he unveiled his plan for a federal United Kingdom today, in a country that he said “appears united in name only”. He called the Brexit vote a “revolt of the regions” and warned: “We could see discontent turn into anger as standards of living fall faster and jobs start to go.”

His idea to mitigate this is for a “people’s constitutional convention” – a slightly woolly phrase that we’ve heard from politicians in the past, which essentially means having a consultation with people from the regions about what they’d like to get out of devolution, and then giving them the money, power and equal footing to do it.

Brown condemned the “dead hand” of government centralised in London, and called for Scotland, Wales, Northern Ireland and the English regions to be given far more power by Whitehall and Westminster – predicting that Brexit could tip the balance even further towards London:

“Inequalities have grown, and I tell you they will continue to grow,” he said. “When Brussels repatriates its powers to Westminster and Whitehall, Britain will become an even more centralised country. Instead of repatriating powers over regional policy, agriculture, fisheries and social funds to London, we should instead devolve them to the regions and nations of the UK.”

He believes that the concept of London’s wealth trickling down into the rest of the country is a myth – it hasn’t worked, and won’t work in future.

It’s a compelling argument. The rest of the country needs to be empowered to fight its corner, rather than tossed some money towards patchy investment every now and again by successive governments that are rooted in the southeast.

But it’s also an argument that would work well politically for Labour, which so far has found it difficult being heard in the Brexit debate. A federal settlement would mean talking to people across the country – something that the Tories will find it tough to counter, as they try and steal the “party of working people” brand from Labour. It would also mean far more power for the increased number of directly elected mayors (most of which are Labour representatives), and Welsh First Minister Carwyn Jones (also Labour).

High-profile advocates of Brown’s idea include Labour MPs Alison McGovern and Jon Trickett – from very different wings of the party, suggesting an appetite across ideological divides. They will be pushing their party to campaign for a federal plan. Could they succeed? Or is Labour’s leadership wedded to the old-fashioned socialist belief in a strong, centralised state with redistribution?

One thing about Brexit Jeremy Corbyn has insisted upon is that Labour “respects the decision of the British people to leave the European Union”. What he (and, of course, the government) has been less clear about is how to make Brexit Britain work for the people who voted for it. This is his chance to fill that gap, and steal a march on Theresa May.

UPDATE 13:56 3/11/16

Labour’s regional and devolved nation leaders have responded jointly to Brown’s intervention:

“This is an important intervention by Gordon Brown – and one we whole-heartedly support as Labour leaders and candidates across the UK. The UK's vote to leave the European Union will change our country and Labour must respond to this challenge. The social, economic and constitutional inequalities between the constituent parts of Britain are driving a wedge between people and politics – allowing for the rise of populist, nationalist and simplistic solutions that run counter to Labour party values. "The devolution of power and finance is an agenda that Labour must now make its own, just as it has in the past through delivering the Scottish Parliament, the National Assembly for Wales and the Good Friday Agreement in Northern Ireland and the London Mayoralty. "Labour priorities can never be fulfilled whilst power and finance is centralised – and starting today, we intend to work together with other Labour colleagues across the country to develop a people’s Constitutional Convention to start the process of rebalancing our institutions and our economy. Only by achieving a new, fair settlement for all nations and regions can we be sure of saving the UK from further fracture, resisting arguments for Scottish independence and another divisive referendum and tackling rising inequality.”

By First Minister of Wales Carwyn Jones, Scottish Labour leader Kezia Dugdale, London Mayor Sadiq Khan and Labour's mayoral candidate for Greater Manchester Andy Burnham.