The London mayor accused the Conservatives of an “abject failure” to grasp the gravity of the housing crisis.
He said: “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.
“And I’m under no illusion about the scale. The challenge has been decades in the making, but with political will, it can be overcome.”
Sir Keir Starmer said Sadiq Khan would be able to achieve more if there was a Labour government.
The Labour leader said all Mr Khan’s achievements as London Mayor had been “in the teeth of a Tory government.”
As Mr Khan seeks a historic third term, Sir Keir said the mayor had spent eight years “fighting for London with a government that is hostile to progress because of the mayor.”
With a general election later this year, Sir Keir said: “Imagine the transformation if we had a Labour mayor in London, working alongside a Labour government, how much more we could do – at much greater pace – for all of our communities.
“We know that, nationally, the country wants change, you can feel it everywhere you go. Fourteen years of failure and the country wants the chance to say ‘let’s change’.
“They know the Tories can’t deliver that change. Look around you, is there anything now working better than it did 14 years ago? The answer to that question is no.”