The most important result of Thursday’s elections across the UK, the one that will have an enduring impact and great meaning beyond these islands, is the election of Sadiq Khan as mayor of London. The symbolism is potent. London, the most diverse city on the planet and one of the great cities of the world, has chosen a Muslim as its leader.

What an eloquent rebuttal that is to all those, from Isis to Donald Trump, who insist there is some fated, and fatal, tension that means Muslims do not belong in western societies, that Muslims and non-Muslims can never live together side by side. While Isis denounce “the grey zone” defined by variety and difference, while the Republican party has chosen as its standard bearer a man committed to barring Muslims from entering the United States, Londoners have chosen the son of a Pakistani bus driver called Khan: a Muslim who has gone out of his way to empathise with all of London’s multiple communities, a Muslim who broke his Ramadan fast in several synagogues. And they did it in defiance of a cheap, race-baiting campaign by Zac Goldsmith that will stain him forever.

Next in significance is surely the result in Scotland, where the SNP have narrowly lost the outright majority they won in 2011 but will remain firmly in charge. They first won power in 2007, and will now keep it at least until 2021. Their command of Scottish politics is dented, but no more. Indeed, through a quirk of the electoral system – and that anorak’s favourite, the d’Hondt mechanism – the SNP lost a handful of seats even though they gained more votes. (They did so well in first-past-the-post constituency battles that they qualified for fewer “top-up” seats under PR.) Simultaneously the natural party of government in Scotland and an insurgent movement, the SNP has a good claim to be the most successful political party in the United Kingdom.

Their only competitors for that title are the un likely runners-up north of the border: the Conservative party. Once an endangered species in Scotland, the Tories will now be the official opposition in that country, led by a woman, Ruth Davidson, whose star quality and appeal across party lines have some UK Tories wondering whether she, rather than the warring posh boys in Westminster, might be the future leader they’ve been looking for.

What is usually seen as a test of strength for the government became framed as a test for Labour

But Scotland conceals a deeper success for the Tories. In government for six years and encountering serious turbulence, they should, by rights, have tanked at these elections. But they didn’t. They held on, losing Worcester council but not much else.

Which brings us to Labour. The oddity of these midterm contests was that what is usually seen as a test of strength for the government of the day became framed instead as a test for Labour. And here opinions divide on factional lines.

For Jeremy Corbyn and his allies, this was a step in the right direction. Labour did well in London, held on to fragile councils in southern England and, best of all, defied the polls that projected council seat losses in the hundreds. Sure, Scotland was a disaster, but Labour held on in Wales and increased its share of the vote on 2015. Consider the terrible publicity of the final few days of the campaign – Ken Livingstone mouthing off about Hitler, a Labour MP calling him “a Nazi apologist” in front of the cameras – as well as the constant incoming fire from the irreconcilables of the parliamentary party and their friends in the press, and, say the Corbynites, it’s a testament to Corbyn that Labour won as many seats as it did. Bottom line: Corbyn’s enemies expected – maybe even wanted – a meltdown and they didn’t get it.

The counter-view is rather less cheery. It begins with the observation that Labour has not come third in Scotland for a century. During last summer’s leadership campaign, Corbyn’s advocates said that shifting left – denouncing austerity, promising to raise taxes and scrap Trident – would bring back those who had defected to the SNP. Scottish Labour followed that advice to the letter, fighting on an impeccably Corbynite platform. And it was trounced.

As for England, the last time Labour in opposition failed to make local council gains was in 1985, when the party had lost two elections and would go on to lose two more. On this measure, there is little comfort to be had in the fact that the losses were confined to double figures. That Labour failed to make gains is indictment enough. Michael Foot managed it, as did William Hague and Iain Duncan Smith. It really is the very least an opposition is expected to do. Not sufficient to gain Westminster power, but certainly necessary.

Sadiq Khan arrives at City Hall with his wife Saadiya (right) and campaign team. ‘The symbolism is potent. London, the most diverse city on the planet and one of the great cities of the world, has chosen a Muslim as its leader.’ Photograph: Stefan Rousseau/PA

Especially when facing an opponent engaged in open civil war. These elections could have been timed to ensure Tory disaster, bang in the middle of a European referendum campaign that has seen a cabinet resignation and daily internal bloodletting, with senior Conservatives regularly tearing down their own leader and each other. There was so much flesh to be pecked off Tory bones that Labour should have been gorging itself. Yet even in these circumstances, after a calamitous budget that sought to rob from the sick and disabled to feed the rich, it was Labour that lost seats.

In the totemic seat of Nuneaton, where Tory victory last May presaged the party’s overall triumph, there was an 11% swing away from Labour and toward the Conservatives. That hardly suggests a party on its way to Downing Street. Similarly alarming are Ukip’s new foothold in Wales and its steady encroachment on to Labour turf in the north of England.

Nor will it do to say that Corbyn did well by seeing few losses from the high-water mark set in 2012, when Labour made 857 gains. For as one observer quipped, if Ed Miliband represents your high-water mark, you need a bigger boat. That 2012 performance came three years before an election defeat. Remaining consistent with that position does not inspire optimism. Remember, without Scotland, Labour needs to be 13 points ahead of the Tories in England to win a general election. And where, incidentally, are those millions of non-voters who, the Corbynites insisted, were turned off by New Labour and Milibandian austerity-lite but would stampede to the polling stations when Jeremy was there to inspire them?

The trouble is, there can be no resolution of this argument. The only way to determine once and for all whether Jeremy Corbyn can win a general election is to let him fight one. Until then, every other supposed test will be imperfect. The way voters choose councillors is not a reliable guide to how they will choose a UK government: if it were, Ed Miliband would be in No 10. And in local contests there will always be mitigating, complicating local factors that can explain away anything.

Besides, you can never be sure if a Labour win is despite or because of the leader. Sadiq Khan distanced himself from, and regularly denounced Corbyn, during his campaign, yet Diane Abbott claimed his projected win was “all about Jeremy”. Both camps will see what they want to see in these results.

For Corbyn’s defenders, it’s obvious. The country is itching to embrace him as its prime minister, if only the embittered refuseniks would stop sniping and get out of the way. For Corbyn’s opponents, the picture is just as clear. Labour is marching, banners bright and in fine voice, off the same cliff it fell from in 2010 and 2015. This argument will not be settled until 2020 – but by then it will be too late.