How can this disunited kingdom be brought back together?

However much we are told by politicians that this week’s local elections are about bins rather than Brexit, it would be odd not to use the results to take the temperature of the nation. These are real votes, after all, rather than an opinion poll.

There were some surprises – many had expected Labour to gain significant ground after a month marked by the Windrush scandal and the resignation of a home secretary. Even without that, the electorate often chooses to give the government a bloody nose when the consequences are not as heavyweight as those of a general election. But these results tell us something less unexpected too: this is a nation still divided and ill-equipped for the challenge of Brexit.

After the 2016 referendum, which split the nation by 52 per cent to 48 per cent, and the 2017 general election, which resulted in a hung parliament, the BBC’s projected national share of the vote from the English votes on Thursday was: Conservative 35 per cent, Labour 35 per cent and Liberal Democrats 16 per cent.

Just to give some idea of what that might mean, the BBC and Sky News projections for the House of Commons put the Conservatives well down on their result last year. Of course, we must take this projection with a pinch of salt, but that would mean Theresa May needed the support of more than the Democratic Unionist Party to remain as prime minister. Given how bruised Lib Dems still are by their experience of the coalition, that would probably mean Jeremy Corbyn as prime minister, supported – or at least enabled – by the Lib Dems and the Scottish National Party.

This hardly seems stronger or more stable than Ms May’s weak and wobbly government. It is a worrying sign of the failure of our politics and our political leaders. At a time when the country needs to be brought together, it seems that the leaders of the two main parties are intent on defending their own base and keeping the country divided.

Of course, democracy by its nature is divisive. It is, and it ought to be, a robust argument about the way forward, often portrayed in simplistic terms. But it ought also to be a platform for leadership, and, if we judge success by more than just winning an election, successful leaders have to appeal across traditional boundaries. Neither Ms May nor Mr Corbyn have shown themselves well suited to that task. Instead, we have two political leaders struggling to unite the factions among their supporters and indeed among their own MPs, let alone leaders compelling enough to tempt large numbers of voters to switch from left to right or vice versa.

They have left the centre ground a barren place, populated by many voters who feel alienated from both main parties. For that reason, The Independent welcomes the strong showing by the overlooked Liberal Democrats. It is easy – and not necessarily unfair – to cast their efforts to rebuild in the wake of the coalition as rudderless. But Thursday’s results (even allowing for the Lib Dem tendency to perform better in local government than general elections) do show a surprise: their split of the national vote would leave them with around another 14 MPs, more than doubling the current figure. And, in these turbulent times, that is not insignificant.

The bigger picture for the party is that, under Sir Vince Cable, it has not been able to speak up more compellingly for the 48 per cent who voted to remain in the European Union. Labour – or at least Mr Corbyn and his inner circle – has not chosen to be the party of the 48 per cent. The Lib Dems were presented with this opportunity on a plate, yet still they have not managed to make a huge impact at the polls. The point stands: with the “dominant” party losing dominance, a small electoral success in the centre ground could be meaningful.

The role of Labour and the Liberal Democrats over the next few months, meanwhile, will be to try to encourage centrist Tory MPs to push the government towards a softer Brexit, primarily by keeping Britain in a customs union with the EU. Leverage is everything. It is not inconceivable that even slight evidence of returning strength could make a difference.

However, the clearer, crisper lesson from Thursday’s elections is that both main parties lack the kind of leadership that can reach beyond the diehards and tempt voters across both sides of the centre ground. The Conservatives’ support appears to map strongly on to pro-Leave areas. Will Ms May feel the pressure to deliver the hard Brexit that her people want, even though her opinion at the time of the referendum was that we should remain in the EU?

At a time when a potentially disastrous vision of Brexit is still very much possible, strong leaders are needed to do what is right. And to build unity around their vision to heal the scars of a divided kingdom.