Sadiq Khan accused the Tories of an “abject failure” to tackle the housing crisis as he launched his mayoral campaign with a pledge to build 40,000 new council homes by the end of the decade.

In a speech on Monday alongside Sir Keir Starmer, he said London would go “much further, much faster” with Labour running both Downing Street and City Hall.

Mr Khan promised to unleash “the greatest council housebuilding drive in a generation” and to double his previous goal to start building 20,000 council homes, which he hit last year.

Describing the mayoral election on May 2 as a “two-horse race” and the “closest contest ever” between himself and the Conservatives’ Susan Hall, he said the vote would “determine whether London’s brightest days are ahead of us or behind us”.

Mr Khan touted the “rare, precious” prospect of Labour rule in both Downing Street and City Hall, saying Sir Keir’s victory at the general election would mean the capital could “go from rowing against the tide of a Tory government to having the winds of a Labour government at our backs”.

In a plea to voters to re-elect him, the mayor said this presents a “once-in-a-generation opportunity to make real inroads into solving London’s housing crisis” and “end the scandal of rough sleeping”.

He said: “There’s been one constant – on abject failure on (the Conservative government’s) behalf to appreciate the gravity of this crisis. We saw it when the last home secretary claimed homelessness is, quote, a lifestyle choice. We saw it last week when the latest housing minister said housing is never really the problem.”

In a display of strengthened ties between the London mayor and the Labour leadership, Sir Keir described Mr Khan as “my friend Sadiq” with whom he could “bring about huge change” as he spoke at the campaign launch in central London.

“The idea of me working with my friend Sadiq across London, the mayor of London and a Labour government working together – that will transform so many lives,” he said.

Sir Keir also praised the mayor’s commitment to clean-air, after last year refusing to back the expansion of the ultra-low emission zone (Ulez) and calling on Mr Khan to “reflect” on the policy.

“I say to people who challenge me on cleaner air, I’ve got two kids. They’re 15 and 13. I wouldn’t give them dirty water to drink and I wouldn’t want them to breathe in dirty air,” he said.

Mr Khan said that working together with a Labour government, “we can go even further, quickening the pace, building on the progress we’ve made and unleashing the greatest council housebuilding drive in a generation”.

“After years of a Tory government trying to drag London backwards, a Labour government would be transformative, propelling us forwards and helping to accelerate delivery of the homes Londoners desperately need and deserve,” he said.

Amid concerns he could lose to the Tory candidate because of changes in the voting system, Mr Khan will highlight that his main opponent Ms Hall voted against his free school meals programme for all primary pupils and his Transport for London fares freeze.

In previous contests, Londoners have been able to express a first and second preference, but this year’s election will be held under the first-past-the-post system, meaning voters will get only one vote each.

The Labour leadership has refused to commit to free school meals, emphasising instead its pledge to introduce breakfast clubs in a bid to address child hunger.

Asked whether he envisaged problems emerging from the difference between his policy and Sir Keir’s position, Mr Khan said: “Keir Starmer, Rachel Reeves, Angela Rayner, the entire shadow cabinet are united in their support for devolving more powers and resources to cities and regions across the country.

“What’s right for Redbridge in London might not be right for Redcar. What’s right for Bermondsey might not be right for Birmingham. And so I’m quite clear – it’s not a one-size fits all solution.”

In a pitch to “fellow progressives”, Mr Khan launched what he described as a “love letter” campaign to persuade supporters of other parties to “lend him their votes”.

He ended his speech by praising the capital’s diversity, saying: “I’ve never stopped standing up for London’s values of openness, equality and inclusion, striving to unite London’s communities, not divide them, celebrating our diversity, not denigrating it.

“Because let me be clear – London’s diversity isn’t a weakness. It’s a formidable strength. And it makes London not only special, but the greatest city on Earth.”