As Labour members prepared late last summer to elect Jeremy Corbyn as leader, Gordon Brown warned in a speech that: “Making what we want — the desirable — possible means making the desirable popular and electable.”

Sadiq Khan, who has succeeded Boris Johnson as London Mayor, is both popular and electable, and now has the largest personal mandate of any elected politician in the United Kingdom (more than 1.3 million people voted for him).

Khan is the son of a Pakistani immigrant who worked as a bus driver, as he never tires of saying. He is also an observant Muslim and, in a period of rising xenophobia, a potent symbol of the openness, tolerance and diversity of our capital city.

The triumph of this upwardly mobile mayor, who grew up as one of eight children in a council house, should inspire people from all different ethnicities and backgrounds to believe that, with talent and determination, they too can be elected to the highest offices in the land. The great doors of power are not closed to them after all.

But, on the whole, it was a pretty noxious mayoral election campaign, especially when, in the final weeks, Zac Goldsmith smeared his Labour opponent as a fellow traveller of Islamists. The subtext was obvious: this Muslim called Khan, a former human-rights lawyer who has spoken at public events alongside extremists, cannot be trusted.

Goldsmith traduced Khan but he also underestimated and misunderstood him. Khan is less an extremist than an extreme pragmatist. Above all, he knows how to win, which means at times he can seem like a man for all seasons, courting both the Left and the Right, in the manner of Harold Wilson of old.

I remember Khan telling me when we met for coffee last year that he would comfortably beat Tessa Jowell, the admired Blairite candidate who was then the favourite to become the Labour mayoral nominee. “You’ve got to understand who’s voting in this contest,” he said.

Later, as Labour careered to the Left after the general election defeat, Corbyn would be useful to Khan, who sensed the mood among the party membership. Once Khan won the nomination, however, he astutely distanced himself from the Labour leader, pledging he would be the “most pro-business mayor ever”.

Similarly, Khan never doubted he would beat Goldsmith, even as his opponent, hitherto a charming, liberal Tory environmentalist, was coerced into becoming a mud-slinging belligerent.

Labour people are naturally cheered by Khan’s victory. Some see it as vindication of Corbyn’s leadership and radicalism. They should be so lucky. In bitter truth, last week’s election results in England, Scotland and Wales merely reiterated the depth of the party’s malaise. Labour is the first Opposition party since 1985 to lose seats in local elections.

We already knew from the general election that, in spite of becoming a playground for a deracinated international plutocracy, London is a Labour city. But London is not England, and England is not Britain.

Consider what happened in Scotland, where Labour was once the natural party of government and is now not even the official opposition at Holyrood. That title belongs to the resurgent Tories, led by Ruth Davidson, whose charisma and blue-collar conservatism as well as Labour’s mediocrity have inspired an improbable revival of the party of Margaret Thatcher in Scotland.

It’s a myth that the Scottish people are more Left wing than the English. They disliked Thatcherism certainly, but few of them yearn for Corbynite socialism. What powers the SNP’s popularity is nationalism, a botched devolution settlement that allows the nationalists to claim all successes as their own while attributing failures to Westminster, and the slow death of Scottish Labour.

The former SNP leader Alex Salmond is a centre-Right nationalist, a former oil economist and an instinctive tax-cutter. His cocky, competent successor as leader a nd First Minister, Nicola Sturgeon, is a pro-business centrist with a social conscience and a long-standing aversion to nuclear weapons being located on the River Clyde.

Misreading her own country, Kezia Dugdale, leader of Scottish Labour, opted to challenge the SNP hegemony by moving sharply to the Left. She proposed raising income tax even for low and average earners (never sensible) and equivocated over her party’s commitment to the Union. Labour was crushed and the Tories under Davidson are now claiming to be the last, true believers in, and defenders of, the Union in Scotland.

Where does all this leave Jeremy Corbyn? One source close to the small cohort of Left-wingers who are in control of the party told me that the Islingtonian dislikes the burden and intrusions of leadership and is open to the possibility of John McDonnell, his long-time ally and shadow chancellor, succeeding him in the right circumstances. But first, the Left wants to take full control of the party’s policy-making mechanisms and enact a final revenge on Tony Blair and his few remaining disciples, whom they despise.

If what Sadiq Khan describes as his “big tent” politics represents the best of London Labour, Corbyn and his closest allies — sectarian, ideologically inflexible, suspect on patriotism, drearily pious — represent the worst. In an article yesterday Khan warned Labour that “we will never be trusted to govern unless we reach out and engage with all voters — regardless of their background, where they live or where they work”.

The new Mayor might as well have been talking to his wife because Corbyn has no desire to listen or reach out as instructed. He’s less a “big tent” pragmatist than a closed-minded ideologue, a serial rebel who somehow, late in life, became the accidental leader of the opposition. He knows he doesn’t have the support of most of his MPs, who are frankly embarrassed by his incompetence and cranky obsessions.

But he has the support of the members and activists, which means he is immoveable. Meanwhile, the Tories are free to feud, U-turn at will and contradict each other over Europe, knowing full well that Labour’s zombie opposition cannot hurt them.