Boris Johnson has accused the chair of the UK Statistics Authority of being a "Labour stooge".

The London mayor's attack came after he was put on the rack over misleading statistics he had given to a Commons committee to highlight the success of an initiative to cut crime.

Johnson hit out at Sir Michael Scholar, who served as private secretary to former Tory premier Margaret Thatcher in the early 1980s, after being questioned by the London assembly about his use of inaccurate figures suggesting a dramatic cut in reoffending as a result of one of his crime-cutting schemes.

The 30-bed Heron Unit at Feltham Young Offenders Institution is funded by the Conservative mayor and offers prisoners extra support in a bid to curb reoffending after their release.

Johnson had compared a 19% re-offending rate among those released from the unit to a national average of around 78%.

Scholar, whose organisation is directly accountable to parliament, last month wrote to Keith Vaz, the chair of the home affairs committee, to tell him the figures Johnson had quoted to a panel of MPs "do not appear to stand up to scrutiny".

He wrote: "The mayor's evidence to your committee is not supported by the Ministry of Justice's published statistics … nor is it supported by any statistical analysis published by the mayor.

"Advice about the limitations of the figures was not followed. The comparisons that have been made between national reoffending rates and reoffending rates at the Heron Unit are inappropriate – it is not explained that these comparisons do not control for the different characteristics of offenders.

"It would assist informed public debate on this matter if there were a proper presentation of the relevant statistical material."

He said the work of the mayor's office is not covered by the Code of Practice for Official Statistics, and that Johnson had "declined my request that he should voluntarily undertake to conform with the requirements".

Two weeks ago a Greater London Authority officer admitted to an assembly scrutiny committee that the latest figure on reoffending for May was actually 39.7%.

Labour's Joanne McCartney said officials had warned that there were a number of caveats around the low figure, saying it was "based on anecdotal information and does not represent a reconviction rate, and should not be used publicly".

Johnson said he had used the figure to highlight the scheme's success to date. He admitted he had failed to make clear to the Commons committee that the figures were "provisional", but denied he had misled the Commons committee.

He told the London assembly: "There's this guy Scholar writing me letters who sounds … like some sort of Labour stooge."

He added in response to McCartney: "I am not impressed by the conduct of that particular body and its chief, if I may say so disrespectfully. Nor am I impressed frankly by your whole line of questioning, which I think is petty, political and mind-bogglingly trivial by comparison of what to do, which is to change the lives of young people."

The mayor admitted he had been warned that the figure came with a series of caveats and was not confirmed, adding: "If I erred, it was not in saying these figures are temporary, they are provisional, they do not represent a final analysis, and we will have to see how the Heron Unit fares in succeeding years and months.

"I hadn't misled the committee. All I had said was that, to the best of my knowledge … these statistics as I understood them … reflected a success.

"What I was trying to do was to illustrate some of the interventions that you need to deal with young people and stop them going off the rails.

"In the course of a long paragraph of explanation, I used the statistics I had in my head about the success of the Heron Unit, because I want to promote that unit and I want to see more work done like that. And if it means advertising the success, I am absolutely determined to do it."

He said the fact that the actual reoffending rate was 40% was "still an achievement" because it was lower than the national average.

McCartney told Johnson it was impossible to compare the 19% rate to the national average because those at Feltham had been out of prison for only a few weeks. The Ministry of Justice official reoffending rates are based on offenders who had been out of trouble for far longer.

She also pointed out that the national reoffending rate for youths, after their first time in custody, was under 60% rather than 78%.

Speaking after the mayor's question time, McCartney said: "We all want this to work and to tackle re-offending. But wilful misuse of stats in this way makes it impossible to know what's working and what isn't.

"Boris was told not to use these figures, but did so, it appears, to claim a success without any evidence to back it up. It's no wonder he doesn't want to sign up to the rules adhered to by every other government department, but he should do so immediately."

A spokesman for the UK Statistics Authority responded to Johnson's accusation: "The mayor is entitled to his views. The independence of the Statistics Authority and its chairman are evident from our published correspondence and reports."