Sadiq Khan told the Labour shadow cabinet this week that his re-election as London mayor “hangs in the balance” despite polls showing he is about 25 points ahead of his Conservative rival, Susan Hall.

The London mayor told Keir Starmer’s team that he was “under no illusions” he could lose against Hall in spite of his commanding lead, partly because the voting system has changed and new rules to require voter ID.

Labour sources said that in the meeting he had pointed to internal research showing how the introduction of voter ID could cost Labour 5% of its vote.

Khan is overwhelmingly likely to win a third term as London mayor but his camp is concerned about motivating voters to turn out if supporters think his victory is in the bag.

In the last London mayoral contest, Shaun Bailey, the Conservative candidate, came within five points in the first round of voting against Khan unexpectedly, on the back of support in the outer London suburbs.

In this mayoral election, for the first time, there is no second round of voting, after the government abolished the alternative vote system in favour of first past the post.

Khan told Labour shadow ministers that his Conservative opponent has been “mostly invisible” and called on them to help make Londoners aware of what he termed her “backward, divisive views”. He highlighted that Hall has on social media promoted the views of Enoch Powell, and has publicly thanked the far-right commentator Katie Hopkins when she used the term “Londonistan”.

Asked this week by Prospect magazine about the Powell tweet, Hall said: “Well, first of all it was a ‘like’ and I apologise if it offended anybody.”

And on the Hopkins “Londonistan” tweet, and the suspension of the former party deputy chair Lee Anderson for alleging Khan was under the control of Islamists, she said: “I didn’t agree with what [Anderson] said … But do you know what, everybody can go on about those tweets. The truth of the matter is, we are looking to elect a mayor that will put London right … People [are] going on about my Twitter because it’s the only thing you can go on about.”

Asked whether it was a “jarring” endorsement that would alarm Muslim Londoners, she told the magazine: “Jarring is the fact that poor people are having to pay £12.50 a day [the Ulez charge] that they literally cannot afford. That is real. And that isn’t just hurty words.”

A spokesperson for Hall said: “Susan is listening to Londoners. Her campaign is about putting more police on the beat, ensuring women feel safe, scrapping the Ulez expansion and building more affordable family homes. That is our sole focus between now and 2 May.”

The Conservatives have been criticised this week after releasing and then deleting a video that used scenes of a panicked crowd at a New York subway station to criticise Khan’s record on crime in London. Hall’s team were unaware of the video, which was produced by the central party.

The attack ad, posted on X in support of Hall, showed people panicking and rushing through New York’s Penn station after false reports of gunfire in 2017.

The caption on the video claimed that “London under Labour has become a crime capital of the world”, and showed an emoji of a red rose, the symbol of the Labour party, wilting and shedding its petals.

Paul Scully MP, who was a rival of Hall to be the party’s candidate for London mayor, told Times Radio on Thursday that the Conservatives in London should avoid trying to scare people and businesses out of the capital.

He said: “There’s plenty of things to focus on the mayor and call him out on […] without just, sort of putting out a scare video about New York.”

Despite the misstep, George Osborne, the former Conservative chancellor, said on his Political Currency podcast on Thursday that Khan was “more vulnerable than he looks”.

He added: “The complaint from the Susan Hall campaign is that they’re not getting enough support from the Conservative HQ, that the Conservatives’ HQ have given up on the election. I find it just a bit odd that more effort has not been put into this. If you’re Sunak you’re looking for ‘what are the opportunities I’ve got to completely reset things’. And the London mayoral contests you would have thought [could be that opportunity].”

A Conservative insider disputed that account, saying party staff were working for Hall and that she felt fully supported.