King Charles’s warm welcome in Scotland and Northern Ireland during his UK tour cannot mask the fact that he will face a more difficult task than the Queen in holding the union together. It is not impossible that it breaks apart during his reign. It would not be about him; political developments in Scotland and Northern Ireland after Brexit would also have tested to the full his late mother’s powers to keep the UK together. If, as expected, the Supreme Court rules that the Scottish parliament does not have the power to call an independence referendum, the Scottish National Party will make the next general election a plebiscite on the issue. It is not going to go away even if Liz Truss ignores Nicola Sturgeon – her crass promise to Tory activists during the leadership election.

In Northern Ireland, too, Truss will have to cast aside her campaign rhetoric if a deal is to be reached with the EU on post-Brexit rules on goods moving from Great Britain to the North. The alternative – a damaging trade war with the EU and continued paralysis in Northern Ireland’s devolved institutions – could increase public support for a united Ireland.

Having a new monarch makes it a good time to think about the way the UK works – or, more accurately, doesn’t.  As it happens, a draft report on constitutional change is being quietly discussed within Labour’s high command and is due to be published in November.

Gordon Brown, who was asked to review the constitution by Keir Starmer, will propose some new powers for Scotland’s devolved institutions but insist that is not the answer to the independence question. Brown’s commission will outline measures to give Scotland enhanced nationhood within the UK, so its institutions work better and more cooperatively with Westminster to secure a bigger voice in the UK and around the world.

An elected House of Lords would include representatives from the UK’s four nations. Abolishing the unelected Lords, already Labour policy but not always shouted from the rooftops, could cause tension with the King and test his modernising credentials. The Queen was said to be unhappy about the Blair government’s decision to remove from the Lords most members of the hereditary club to which she also belonged.

Brown’s hope is that offering change would appeal to “middle Scotland”, the 40 per cent who are undecided on independence, and even some who currently support a breakaway. However, his report contains more proposals about England than Scotland, because the “English question” is the missing piece of the UK’s devolution settlement.

The former prime minister argues that the path to keep Scotland in the union must include “fixing” England, warning that a very centralised UK will slip further down the international league table without a plan for economic and political devolution to English towns, and groups of councils banding together. He does not advocate a new tier of government or elected mayors for all areas but believes local authorities’ excuses for not working closely with neighbouring councils should no longer be tolerated.

Brown would close the gap between regions by ensuring fair distribution of central government funds. He is right: the current system of councils bidding for money allows the centre to indulge in the pork barrel politics we have seen in the Tories’ drive to “level up”.

Keir Starmer has a dilemma about whether to adopt Brown’s blueprint in full. Its publication, originally due on 1 September, was postponed in the hope he would be able to do so. But some Starmer advisers think there are few votes in talking about dry constitutional matters during an economic crisis.

However, there are strong reasons why Starmer should embrace the Brown plan. Labour does not yet have a convincing strategy for securing economic growth at a time when Truss has made a return to 2.5 per cent growth her key economic goal.

Strangely, Truss has left herself open to attack by apparently dropping Boris Johnson’s levelling up mantra. Of course, she will want to do things differently, but there is a danger of sending the wrong signal to the red-wall constituencies wooed by Johnson in 2019, and giving the impression she is more concerned about the Tories’ traditional blue wall in the south. Some Tory MPs in the north privately fear Truss will not make the same political or financial commitment to levelling up as Johnson did. Her commitment to Thatcherite trickle-down economics and her tax cuts that will hand most to the better off will not bridge the divide between London and the different world of the poorest regions. Brown’s plan would, giving Labour some useful electoral ammunition. Starmer should offer the country more than a slightly nicer version of the status quo and live up to his own billing of the Brown review as “the boldest project Labour has embarked on for a generation”.