Boris Johnson would have been "attempting to pervert the course of justice" if he knew police were actively investigating phone hacking when he described fresh allegations as "codswallop", a member of the Metropolitan Police Authority (MPA) has claimed.

Jenny Jones, a London assembly member for the Green party, made the claim after the mayor's deputy for policing, Kit Malthouse, revealed he was informed that Scotland Yard was looking into claims made in a New York Times article on 10 September last year, five days before Johnson dismissed the allegations as a "political put-up job" by Labour.

The revelation also casts doubt on Johnson's claim, made at a London assembly meeting on 15 September, that he was in "almost continuous conversations" with Malthouse about the phone-hacking allegations "and other matters".

The MPA sought to clarify whether the Conservative mayor, who chose to delegate the chairmanship of the MPA to Malthouse 18 months ago, knew an investigation was active when he dismissed the allegations.

Malthouse initially claimed that he had received no specific briefings on phone hacking and had no discussions with senior officers about it in September.

But he admitted this week that such a briefing had taken place after he "personally" reviewed his diary following a written request from Jones for a full account of what he knew and when.

On Tuesday, Malthouse confirmed that John Yates, then Met police assistant commissioner, requested a phone conversation with him on 10 September, in which he reassured him that he was looking at the allegations that had surfaced in the New York Times.

Central to the paper's report was the claim that Andy Coulson, David Cameron's then director of communications, had "actively encouraged" a reporter to illegally intercept phone messages when he was the editor of the News of the World.

Malthouse said Yates had told him that he was looking at the report and considering whether there was "any new evidence", and that Met officers "may fly to the USA to conduct interviews".

Members of the MPA – the body responsible for overseeing Scotland Yard's work – questioned Malthouse about whether he had relayed the briefing about the investigation taking place to Johnson before the mayor made his comments.

Malthouse said he "didn't recall" whether he had discussed what Yates had told him with the mayor prior to the 15 September session, adding: "I think it is probably unlikely that we did, but I cannot recall precisely."

Jones said it was "inconceivable" that Johnson would not have known this when he dismissed the allegations.

She told a meeting at London's City Hall: "If he did know, he was attempting to pervert the course of justice."

Malthouse told Jones this was a "strong charge" to make and warned that "[you] might be getting yourself into hot water by saying things like that".

He said he believed the mayor had based his views on the briefings and reassurances that had been given in previous discussions, and added: "The mayor is a personality that likes to express himself in particular ways."

A spokeswoman for the mayor dismissed Jones's suggestion as "preposterous".

The issue of whether or not the information received by Malthouse was passed on to Johnson before he faced the assembly also put the spotlight on the mayor's decision to delegate the chairmanship of the scrutiny body to Malthouse.

Joanne McCartney, Labour's lead member on the MPA, said: "The questions about the mayor's role in the police investigation will not go away.

"He said when he stood down that he would remain fully accountable for policing, but we still don't know what he knew or what he was told by his deputy before he decided to get involved in a live investigation.

"It's not the first time he's done this and, given his actions, I think the government should now think long and hard before pressing ahead with their plans to give him more direct power over London's policing."

Yates told Malthouse on the same day that he wrote to the prime minister's chief-of-staff, Ed Llewellyn, offering to "brief" Cameron on the latest phone hacking inquiry, but Llewellyn declined the offer.

The assistant commissioner, who quit last week, wrote to Johnson earlier this month to apologise for failings in his briefings about the police's stance on new phone-hacking allegations that emerged after the original 2006-07 investigation.

He told him: "I have acknowledged now that, with hindsight and with what we are currently seeing, my decisions would have been different. If this has placed you in a difficult position, then I very much regret this."