The figures don’t lie – although they will be endlessly debated. Amid the competing definitions of what ranks as success for a Jeremy Corbyn-led Labour party on May 5, a handful of numbers stand-out.

The share of the vote won in local elections by Opposition leaders who go on to become Prime Minister has hovered around the crucial figure of 40 per cent for several decades.

Of course, the electorate has become more fragmented since John Smith and Tony Blair started eyeing up Downing Street in the 1990s but, what has not changed, is the magic number of 326 seats required to command an absolute majority in the House of Commons.

And you don’t get anywhere near that if your party’s share of the vote is stuck on a per cent figure in the low 30s.

Moving from a one-point poll lead over the Tories to 40 per cent represents a tall order for Corbyn but, as the man who won a landslide victory in the Labour leadership contest after starting as a 100-1 outsider, he won’t be put off.

And he has been given a fair wind by the cocktail of arrogance, indifference and incompetence that has characterised the Tories’ response to the Tata Steel crisis and the revelations of the Panama Papers over the last week. As a backdrop to the launch of the local, London, Scottish and Welsh election campaigns in Harlow today – his biggest test yet as leader – it could have hardly have gone better.

That doesn’t mean things are going entirely smoothly in Corbyn’s own party, however.

When Jon Trickett tried to play down expectations in an article for LabourList yesterday, saying any advance on the party’s showing in the General Election, when it finished 6.5 percentage points behind the Tories, would represent progress, it prompted a swift reaction from the “moderates” on the backbenches. Michael Dugher accused Trickett of “getting his excuses in early” on PoliticsHome while Liz Kendall pointed out that no opposition party has gone on to win a general election after being behind in the first set of local elections in the parliament for 37 years.

Each activist can make up their own minds up what constitutes success for Labour. What cannot be doubted, however, is that the party faces an enormous task to improve on – or even hold – the gains made by Ed Miliband in 2012, when he picked up 800 council seats.

Labour can and should win in London. In Sadiq Khan we are lucky to have an intelligent, likeable candidate who lives in the real world. And we are just as lucky to be facing a poor Conservative candidate, Zac Golsmith, who often seems a stranger to the real world – or, indeed, to the London Underground, about which he failed to answer basic questions today.

But if, on May 5, the result is all about the candidates, then the aftermath will be all about Jeremy. As the vying factions of the parliamentary party set benchmarks for him to achieve (or unattainable targets for him to miss), the post-match analysis is underway before the fixture has even been completed.

It seems a few of the “moderate” MPs, fearing autumn rule changes that could guarantee Corbyn a place on the ballot paper in any future leadership election, are determined to strike against him in May. Many others, however, remain hesitant because they understand Corbyn’s support among the membership is still strong. The latest approach of one or two, of touting Angela Eagle as a “caretaker leader” after a coup, only destabilises the party – regardless of the fact the shadow Business Secretary is an intelligent and decent Labour figure.

At its best moment under Corbyn, Labour has achieved a slender opinion poll lead, and that was following a shambolic Tory Budget, the resignation of Iain Duncan Smith and more in-fighting over Europe. This lead is a stepping stone but fails to put the party on course to achieve the average net gain it has posted in local elections during its Opposition years – of around 300 council seats, according to the Manchester University academic Robert Ford.

So Corbyn must run fast to stand still. His campaign launch today in Harlow, an Essex new town which swung from Labour to Tory in 2010 and then went bright blue in 2015, was solid but underlined the challenge he faces: to win back suburban voters who haven’t backed our party since the days of Tony Blair, the memory of whom Corbyn wants to banish all trace.

Let May 5 be the “turning point” for Labour, Corbyn said today. It looks like it will be, both for the party and for its leader, but no-one knows which way people in Harlow, or Britain, will turn. For Corbyn, a man who has defied the odds once already, he must show he is turning around Labour’s relationship with millions of voters angry with the Tories but frustrated with our own failure to look like an alternative government.