The senior judge leading an investigation into the ethics and conduct of the press in the wake of the phone hacking scandal has reportedly threatened to quit, following a scathing attack on the investigation by Education Secretary Michael Gove.

Lord Justice Leveson complained to the most powerful civil servant in Downing Street, following claims by Mr Gove that the inquiry had created a "chilling atmosphere" towards freedom of the Press, according to the Mail on Sunday.

Leveson reportedly called Sir Jeremy Heywood to ask that the Education Secretary be "gagged", because his comments risk undermining the inquiry.

"Our clear impression was that he was spitting tacks with Gove and was ready to resign unless the Minister was told to shut up," a Government source told the newspaper.

Sir Jeremy is reported to have told Prime Minister David Cameron about the conversation.

Former journalist Mr Gove, who once worked at the News Corp owned Times, told a Parliamentary Press Gallery lunch in February that he saw "dangers" in the inquiry into press cultures, practices and ethics.

Lord Justice Leveson phoned Sir Jeremy within 24 hours of the comments, it was reported.

Later, the pair clashed when Mr Gove was called to give evidence at the inquiry. The Cabinet Minister went on to make an even more robust assessment on the potential outcome of the probe, warning the judge that inquiry recommendations were often "applied in a way that the cure is worse than the disease".

The two clashed when Mr Gove raised concerns about restraints on the "precious liberty" of freedom of speech. In an apparent slap down, Lord Justice Leveson said: "I do not need to be told about the importance of freedom of speech, I really don't."

Prime Minister David Cameron is reportedly aware of the phone call.