Michael Gove highlighted Conservative misgivings about Lord Justice Leveson as he publicly mocked the judge a week before the publication of his report into the future of the press in Britain.

As the leaders of all three main parties gave undertakings to victims of press intrusion that they will respond quickly to the Leveson inquiry, the education secretary joked that the judge should be given "the Bureau of Investigative Journalism award for commitment to truth-telling".

The bureau was behind the recent Newsnight report that libelled the former Tory treasurer Lord McAlpine, precipitating a series of events that led to the resignation of George Entwistle as director general of the BBC.

Speaking at the annual Spectator parliamentarian of the year awards, Gove said: "It's … a pity that His Honour Brian Leveson cannot be here so he could receive the Bureau of Investigative Journalism award for commitment to truth-telling for his wonderful comments: 'I don't really need any lessons in freedom of speech, Mr Gove, really I don't'."

His remarks came as David Cameron, Nick Clegg and Ed Miliband reportedly assured victims of phone hacking in separate meetings that they would not allow Leveson's findings to be kicked into the long grass of a future parliament, according to the Hacked Off campaign. The victims, who included the mother of the missing girl Madeleine McCann, were told by the leaders that they would support the second phase of the Leveson inquiry going ahead once the criminal investigations have been completed, said Hacked Off.

The victims urged the party leaders to work together once Leveson's report is published, and not to divide on party lines. The report is expected late next week. There is a general expectation that the Liberal Democrats and Labour will back Leveson, including proposals for some form of statutory underpinning of independent regulation, so long as it is seen as workable. The Tory position remains opaque, although Cameron has backed fines and a right of reply.

But Gove and Boris Johnson, the London mayor, made clear that many Tories have grave reservations about the Leveson inquiry. Johnson, who was made politician of the year at the Spectator lunch, was warmly applauded by Gove when he said: "MPs, ministers and all the rest of it – don't you for one moment think of regulating a press that has been free in this city for more than 300 years and whose very feral, fearlessness and ferocity ensures that we have one of the cleanest systems of government anywhere in the world. Very little financial corruption. And which ensures, by the way, that London not only put on the greatest Olympic Games that have ever been held but is also the greatest city on earth to live in and to invest in."

Gove's decision to mock Leveson in public shows he is spoiling for a fight with the judge who summoned him to give evidence after the former Times journalist warned in February of a "chilling atmosphere towards freedom of expression which emanates from the debate around Leveson". In his appearance before the inquiry last May, Gove warned that statutory regulation of the press could threaten "precious" freedom of speech. He cited on Wednesday that his remarks provoked the intervention by the judge.

Downing Street distanced itself from Gove's remarks. The prime minister's spokesman said: "I don't think I have anything to add to those comments."

Asked whether Gove spoke for the government, the spokesman said: "He does – on education."

Labour sources expressed concerns about Gove's decision to confront Leveson in public as victims of press intrusion were meeting the main party leaders.

Speaking before the release of Gove's remarks the founder of Hacked Off, Brian Cathcart, said: "There is a danger that in this debate that the voice of the victims can be lost when we hear the voice of the press very loud."

He added: "All the leaders understood the importance to hear from the sufferers and we have proposed to all of the leaders that when the Justice Leveson has reported they meet the victims again.

""They all recognised the vital need for radical change in the way the press is regulated and all the leaders agreed that the best way forward is an all party approach. We urged them to meet as soon as Leveson has reported to meet on an agreed approach."

Christopher Jeffries, falsely identified as a murder suspect last year said the meetings were "very encouraging since all three leaders made it clear that the status quo cannot be allowed to continue and the old system of press self-regulation has failed and has to be replaced". He added: "They were all on record as saying that on the assumption Leveson's recommendations are proportionate and workable then they will aim to work together to implement those proposals."

Margaret Aspinall, of the Hillsborough Support group, said: "We have to make sure there is no intrusion of private lives especially when it comes to people who have lost."