The survey, published in the Times and conducted by Redfield and Wilton Strategies, shows the Labour incumbent winning just 33 per cent of the vote, with Conservative candidate Susan Hall close behind on 32 per cent.
The polling of 1,100 London voters also showed that if Jeremy Corbyn decides to run as an independent, it could cause Mr Khan to lose to Ms Hall, with her winning 30 per cent and the mayor taking 25 per cent. The former Labour leader would win 15 per cent.
Mr Corbyn, who has been barred from standing for Labour in his parliamentary seat of Islington North at the next general election, has refused to rule out a run for the mayoralty.
It is widely thought however that he is more likely to run to be an independent MP in his north London constituency.
Elections to City Hall previously used the supplementary vote system, with voters able to give a first and second preference for mayor.
If Mr Corbyn does not stand, Mr Khan’s suggested vote share would be a drop of seven points from his result in the 2021 election, where he received 40 per cent of first preference votes.
Ms Hall would also perform less well on vote share than previous Tory candidate Shaun Bailey, coming three points lower than Mr Bailey’s 35 per cent.
But she would come considerably closer than her predecessor to unseating Mr Khan, indicating a tighter election than any seen since the mayoralty began in 2000.
Neil Garratt, the London Assembly’s Tory group leader, said the poll showed “the Labour mayor's bombastic smugness coming home to roost, as Londoners look to a Conservative mayor who will focus on doing a good job for our city.”
Mr Khan dismissed suggestions that he was worried. “Polls go up and down,” he told the Standard. “I have been in politics long enough to realise: never get too excited when you are miles ahead; never get too despondent when you are behind.
“The key thing is this: this is a reminder that the next mayoral election is going to be a two-horse race. Only two people can win this – me or the Conservative candidate. That is why I am encouraging Londoners to lend me their vote if they want a city that is greener, fairer and safer.”
Mr Khan pointed to the ultra-low emission zone (Ulez) expansion across Greater London, the free school meals he is funding for a year for all primary school children in London and the roll-out of 4G and 5G on the Tube and Elizabeth line as policies on which he planned to campaign.
He said: “Whether you used to vote Conservative, used to vote Lib-Dem, used to vote Green – whatever party you used to vote for in the past, lend me your vote to make sure we can build on the progress we have made.”
The pollsters also asked the same set of Londoners how they will vote in a general election. The poll showed 47 per cent support for Labour and 27 support for the Conservatives - suggesting that in the capital, Mr Khan is much less popular than his party, while Ms Hall is more popular than hers.
The mayoral poll also showed the Liberal Democrats winning their best result since 2004, and coming ahead of the Greens for the first time in more than a decade. It projects the party on 16 per cent, or 15 per cent if Mr Corbyn stands.
The Greens appear meanwhile set to be pushed into fourth place on nine per cent or six per cent respectively.
Reform UK - formerly known as the Brexit Party - would win four per cent or five per cent respectively.
The survey also reveals that Londoners remain divided over Mr Khan’s Ulez expansion, with 39 per cent saying they are in favour, and 38 per cent opposed.
Nearly half of Londoners — 49 per cent — meanwhile said they agreed with the former Conservative leader Sir Iain Duncan Smith’s endorsement of Ulez enforcement cameras being saboaged.
The Daily Mail published quotes from the Chingford and Woodford Green MP in which he said he was “happy” for his constituents to “cement up the cameras or put plastic bags over them” because “they are facing an imposition that no-one wants and they have been lied to about it”.
Sir Iain later told the Standard he “does not condone law breaking of any kind”.