You might think a byelection showdown between two progressive parties is unimportant when the deep struggle for the national heart is between the right bloc and the left – but the result in Holborn and St Pancras matters. It matters for Andy Burnham and Labour because this is a test of the Burnham bounce: he saw off the right in Makerfield – can he win over the left too? Can he show he has enthusiastic approval from voters in southern constituencies as well as those in the north?

For the Greens it matters almost existentially because failing here could send them and their leader, Zack Polanski, back to the political fringes. Holborn and St Pancras, neighbouring Westminster, was vacated (vengefully) by Keir Starmer last week. This plum forever-Labour constituency has attracted 96 Labour applications for selection day on Wednesday, though not, it seems, nationally recognised names.

This is Labour’s to lose. And it might. The constituency was comfortably won in 2024 by Starmer; in May’s local elections the Greens took extra council seats, though Labour kept control and remained ahead by 10 percentage points. But byelections are idiosyncratic beasts in which voters risk nothing, electing neither council nor government. Few bother to turn out. For those who do, a byelection offers a free hit for whimsical preferences, “sending messages” on maverick issues or an urge to biff the government of the day.

A Labour loss would dent Burnham’s bounce, letting air out of his optimistic bubble. But frankly, losing here would be no great surprise. Peter Kellner, former president of YouGov and a leading psephologist, lives in this constituency, as do I. While most early opinion makes Labour the frontrunner, Kellner thinks that underestimates the byelection effect. He expects a Green win in a close call: “This is just the kind of seat a Labour government loses,” he tells me. In a metropolitan district with disproportionately young voters, the left is liberated to protest against anything disappointing in a Labour government.

Demographics favour rebellion for a rainbow of reasons in an extraordinarily socially mixed seat. You see vox-poppers choosing its picturesquely famous spots – the pastel houses in Primrose Hill where Paddington Bear lives in the films, the bars and cafes of Camden and Kentish Town – as photogenic backdrops to their reports. But, such elegant streets may be deceptive given that only a quarter of residents are homeowners, compared with 62.5% across England and Wales.

Here 43% live in social housing: Camden has a decades-long tradition of good housebuilding, thanks to a well-run council under great social pressure. The constituency is home to both deprivation and high numbers of graduates; many ABC1 voters and 45% born abroad.

Leaflets saying only the Greens, or only Labour, can win here are arriving through letterboxes – and it’s true, no one else is likely to. That Polanski is seeking the nomination boosts the Greens. Tot up issues where they challenge Labour, and many resonate with the student population. They oppose nuclear weapons and seem divided over increased defence spending. They back rent controls that Burnham has rejected. They oppose Jackdaw and Rosebank North Sea oil and gas drilling, which may both be approved any day now. They want rapid nationalisation of utilities, where Labour hesitates. Locally they campaign on crime, mobile phone thefts and housing.

But it’s Gaza that may shift votes from Labour to Green: in the 2024 election, Starmer’s vote share was slashed and a pro-Palestinian, independent candidate came second with 18.9% of the vote. Arresting thousands for terrorism for silently holding placards supporting Palestine Action is another gift to the Greens. Labour instead points to impossible promises in the party’s £160bn tax, spend and borrowing pledges.

The Green campaign asks: “Why elect just another Labour MP, when a Green MP in parliament will challenge the government?” But this week Labour looks set to select not just “another Labour MP” but Sagal Abdi-Wali, Camden council’s leader and community organiser, popular with her party and a well-known dynamic force locally. Green criticism of Labour over Gaza comes up against a hijab-wearing Muslim woman who has spent years calming racial and religions tensions, and building relationships with many Jewish voters here, too. “If Greens stir up community antagonisms over Gaza,” she says to me, “that would be disgraceful”.

Reform has no foothold here but its attacks on her from afar may galvanise Labour people to come out and vote. Its poisonous home affairs spokesperson Zia Yusuf spits out Reform’s usual ethno-nativist bile, pointing out on X that Abdi-Wali “was born in Somalia. Do you understand what’s happening?” Georgia Gould MP, former Camden council leader, ripostes on X that she “has dedicated her life to public service” and is “the elected leader of Camden council, a community where she grew up and has lived for 35 years” who “embodies the best of our values … an outstanding example of British success”. Telegraph headlines similarly define her primarily as a “Somali refugee”. All this will remind Labour voters that fighting off the racist right is Labour’s great cause.

On the doorstep with Abdi-Wali, in a social housing estate, I saw how she is known and liked for her community work. She takes notes of people’s problems, from housing repairs to e-bikes blocking the road, her local campaign matching Burnham’s localism. But we also meet a college lecturer, who had a run-in with their employer over Gaza, who will “never vote Labour again”. Not for Abdi-Wali? It’s all about Palestine.

Nonetheless, Polanski takes a big risk here after sliding in the polls. For Labour, the challenge is to show how Burnham’s raft of positive policies can ward off hopeless wishes and still reach the left with his hopefulness.