The mayor of London has said the Gorton and Denton byelection has exposed a “far-reaching change and fracturing” in UK politics and Labour must ditch its “flawed strategy” of taking liberal progressives for granted.

In what appears to be an attack on Keir Starmer, Sadiq Khan challenged the prime minister’s branding of the Green party and its policies as “extreme”, saying many of its supporters shared Labour’s values but were disappointed in the government.

Plumber Hannah Spencer overturned a Labour majority of more than 13,000 to become the Green party’s fifth MP. Her party has enjoyed a rise in popularity under its new leader, Zack Polanski, attracting many disaffected former Labour supporters.

The Labour candidate, Angeliki Stogia, came third, just behind Reform UK’s Matt Goodwin, in one of the most humiliating byelection results in Labour’s history.

Labour insiders have long warned that the party risks losing support on the left as it attempts to combat the rise of Reform UK.

Polanski has criticised Labour for its recent hardline immigration policies, claiming the party was echoing “the racist rhetoric of the far right”. The home secretary, Shabana Mahmood, is expected to double down with planned changes to asylum policy.

Writing for the Guardian, Khan said that trying to compete with Reform was inauthentic and a betrayal of Labour values, and warned that the party faced catastrophe in the May elections unless it changed course.

Khan said: “There’s no sugar-coating what happened in the byelection in Gorton and Denton – it’s a terrible result for Labour, coming third in a seat that we had held for nearly a century.

“People often exaggerate the significance of byelection results, but this one does speak to a far-reaching change and fracturing in our politics, which cannot simply be ignored or wished away.

“A political strategy of taking liberal, progressive voters for granted is clearly flawed. The national Labour party and government doesn’t just need to reflect on this result, but fundamentally rethink its approach.”

While falling short of calling on Starmer to step aside, Khan criticised the prime minister for suggesting Green voters were extreme in light of the defeat.

“The vast majority of those who are thinking of voting Green are not extreme,” Khan said. “Many share our values and hopes for the country, but are disappointed with the government. Calling them extreme will only turn more people away.

“The threat to the Labour party is now existential in parts of our country. Without a change in course, we risk a repeat of losing large Labour strongholds, like London, just as we did in the 2000s in Scotland,” he said.

“If we don’t unite progressives, we risk opening the door to the darkness and division of Reform – a party that takes Donald Trump as its inspiration and has promised an ICE-style force on Britain’s streets, which will send shivers down the spine of every minority community living in this country.”

Khan said that at the 2024 mayoral election, he “stood on the promise to stand up for our values of equality, inclusion and respect for diversity”.

He said this meant calling out Trump for racism and sexism, and lobbying for the UK to rejoin the EU customs union in the face of damage done by Brexit.

Khan said: “Staying quiet on these issues and trying to compete with Reform on the right of politics not only feels inauthentic – at a time when authenticity is more prized in politics than ever – but a betrayal of what Labour is supposed to represent. We must address the concerns and fears of voters, not play on them.”

He added that he was not calling for Starmer to resign, but felt his “good work” as prime minister had been overshadowed by “missteps and political positioning”.

Starmer could face a leadership challenge after the local elections in May, unless the party enjoys a significant reversal in its fortunes. Labour is expected to lose hundreds of council seats in England, as well as suffer bruising defeats in elections to the Scottish and Welsh parliaments.

Khan added: “It would not be in the national interest to create political instability at the top of government at a time when there’s so much uncertainty in the global economy and geopolitics.

“But there does need to be real change and a vision that provides hope for the future, not doom and gloom.”