I have never trusted opinion polls less than I do now. Part of that is bitter experience, after polls proved their fallibility in 2015, 2016 and 2017. Part of it is a more specific lesson taught by the US presidential election three years ago, when Hillary Clinton learned to her cost that a hefty national poll lead means nothing in a contest that is settled one state at a time. This logic applies in spades to a UK election, which is not won nationally but seat by seat by seat.

The importance of that enduring truth was brought home afresh last weekend as I tramped the streets of Enfield Southgate, the marginal London suburb won from the Tories in 2017 by Labour’s Bambos Charalambous, best known for a rather wonderful meme in which John Bercow incants the MP’s name to the tune of Queen’s Under Pressure. I followed him for an afternoon’s canvassing, a session that would prove to be a masterclass in the inherent unpredictability of politics.

The seat has a Greek Cypriot community of about 6,000, a number comfortably greater than Labour’s majority in 2017. Charalambous was greeted several times that afternoon in Greek, embraced as a favourite son by those whose pride in him as the first MP from their community was clear. Surely, I asked him, that bloc of 6,000 would give Labour a defensive wall, one that even a national Tory tide would find hard to breach.

The candidate was about to answer when we encountered Christo, a 70-something man repairing a dodgy backdoor who, moving between English and Greek, announced that his number one objective was stopping Brexit, which he considered the biggest mistake his adopted country had ever made. He couldn’t vote Labour, he said, because Jeremy Corbyn had failed “to come off the fence” on the great EU question. He would be voting for the Liberal Democrats. Charalambous pleaded with Christo: that would let in the Tories. But it was no use.

In other words, nothing is straightforward. You might think the Labour incumbent would have a home advantage with those 6,000-odd voters and yet that same group is likely to be less forgiving than others of Labour’s Brexit stance. Charalambous was also sent away with a flea in his ear by several Jewish families, one all but pushing him off the premises, loudly telling him it was “disgusting” that he could work for “someone like that”, referring to Corbyn. There are perhaps 1,500 Jews in Enfield Southgate.

The Liberal Democrats are fighting a weak campaign, which will help the Tories in some places but should also allow Labour to hold on to more of its remain vote

And those are just two of the multiple gusts that might shift votes in one corner of a single seat. There will be equivalent wind patterns in every constituency in the land, each one a microclimate of its own. To take one example almost at random: the Welsh seat of Ynys Môn is a natural, winnable Tory target, but the Conservatives there have selected a Londoner who doesn’t speak Welsh to represent a constituency where 35% name Welsh as their first language. No matter that UK-wide polls might register Ynys Môn as a likely Tory gain, the voters there could beg to differ. As Charalambous puts it, on 12 December “there will be 650 local elections”.

Put another way, a double-digit national Tory lead won’t matter a jot unless it translates into the Conservatives winning specific seats currently held by Labour. Piling up votes where they’re already strong, fattening already-plump majorities, will count for nought. Nigel Farage’s decision not to contest Tory-held seats will help achieve the latter outcome, but might not do enough to ensure the former. On the contrary, the Brexit party risks siphoning off leave voters in historically Labour seats, people who might otherwise have been forced to break the habit of a lifetime and vote Tory.

Each one of those Labour citadels will have its own deeply entrenched resistance to a Conservative wave, allegiances and aversions developed over many decades. They might get over those reservations, as national polling suggests they will, but as we learned in 2017, those seats can be obstinately elusive for Tories. Add to that the likelihood that the Conservatives will lose at least some of their 13 seats in Scotland, as well as in remain-voting parts of London and the south, and you can see why the Tories’ own campaign manager, Isaac Levido, warns that their path to victory is “steep and narrow”.

That’s because of what is perhaps the most crucial fact about this contest, which is that the two main rivals are running towards different finish lines. To be sure of reaching Downing Street, Boris Johnson has to sprint to an overall majority: he cannot rely on help from the smaller parties. Corbyn’s winning post is in a different place.

It doesn’t matter that the psephological sage John Curtice rates Labour’s chance of winning a majority at close to zero, because Corbyn doesn’t need to win a majority. If he can just do enough to deny the Tories an overall majority, he could turn to the SNP, Plaid Cymru and others to push him across the line. He might not need to gain many seats; he might not even need the help of the Liberal Democrats. Put simply, Labour, too, has a steep and narrow path to Downing Street – steeper than the Tories’, given the polls, but smoother in the sense that while Johnson needs to win at least 321 seats to stay in No 10, Corbyn could get there with as few as 270.

‘Johnson has to sprint to an overall majority: he cannot rely on help from the smaller parties.’ Boris Johnson visits a washing machine factory in Newton Aycliffe, County Durham. Photograph: Stefan Rousseau/PA

He’s being helped in that effort by some jaw-dropping, unforced Tory errors. Slow to act on floods in Yorkshire, the Tories once again showed their compassionate side this week when Dominic Raab defended a government decision to seek legal costs from the parents of Harry Dunn, who was killed in a collision allegedly involving the wife of a US diplomat. And the dishonesty and deceptions keep coming.

Meanwhile, twice as many young people have registered to vote this time as in 2017 and the NHS has pulled ahead of Brexit as the most important issue for voters – both of which should make the terrain more favourable to Labour. At the same time, the Liberal Democrats are fighting a weak campaign, which will help the Tories in some places but should also allow Labour to hold on to more of its remain vote. Still, the problems for Labour are the same as ever. In Enfield Southgate, the most common complaint from voters is about the party leader (though there’s no love for Johnson). If it’s not antisemitism, it’s the perception that Corbyn is weak and indecisive. “He’s been swinging this way and that,” one man says. With a sigh Charalambous admits that the leadership question “comes up again and again, unprompted”.

Perhaps Labour’s manifesto can cancel out those concerns, its promises so arresting that it will sweep away wavering voters’ doubts. It’s clear the already-converted love it, even if some might find Corbyn’s talk of a wholesale restructuring of society alarming. The proposals in it, including the major renationalisations, poll well. The problem, as Curtice argues, is that voters don’t yet believe Labour “is actually capable of implementing them”. I’m told that at one focus group in a northern Labour seat this week, the party’s free broadband offer was “laughed out of the room”.

So, yes, there is a path that could take Labour to Downing Street. The trouble is, it’s not just steep and narrow – there are rocks in the way that are stubborn and heavy.

• Jonathan Freedland is a Guardian columnist