Evgeny Lebedev, the eldest son of the owner of the Independent and the Evening Standard, believes the Press Complaints Commission has not shown itself "fit for purpose" during the phone-hacking affair and that he and other newspapers should get together to propose regulatory and legal reform. The 31-year-old son of Alexander Writing in the Guardian today, Lebedev – who manages his father's newspapers day to day – describes the hacking affair as "one of the biggest scandals in public life for decades". He argued that the Metropolitan police also had questions to answer for the way it has investigated the affair.

Asked whether the PCC was "fit for purpose", he said: "Its recent conduct is not proof of that."

He also noted that the Metropolitan police commissioner, Sir Paul Stephenson, "recently said he would rather his men were investigating more serious crimes like robbery", and asked: "But isn't the theft of private information still theft?"

Last week Lebedev, who has recently taken British citizenship, made Chris Blackhurst the editor of the Independent. Blackhurst takes over from the long-serving Simon Kelner, who had been editor or editor-in-chief of the Independent for 13 years.

However, if Lebedev was critical of newspapers involved in hacking – he chose not to name the News of the World – he defended the tabloid media in their battles against the use of privacy injunctions by celebrities to conceal their identity, even if he "despaired" of the "sensationalism" of the news stories concerned.

"If red-top values are the price we pay for an open society," Lebedev said, "then I would rather that, with all the attendant controversy and prurience, over the closed minds bred by a less free press."

He added: "As a British-Russian son of an ex-KGB officer, I feel strongly that one of the best measures of a strong healthy society is its view of free speech." Twitter and Facebook, Lebedev argued, made "the idea of a privacy law … impracticable and naive". This was demonstrated by the Ryan Giggs affair, which saw him repeatedly named on social media sites even though he had won injunctions preventing his name appearing in newspapers.

Lebedev also argued that it was right that the public should be allowed to know about an alleged affair conducted by the former chief executive of the Royal Bank of Scotland, Sir Fred Goodwin, when he ran the bank – even though Goodwin initially tried to use an injunction to keep his name out of the public domain.

The combination of the PCC's performance over phone hacking and the privacy injunction crisis meant that it was necessary to ensure that "our laws catch up with the digital revolution and that our journalists uphold the highest standards".

In the light of such issues, Lebedev said he "would like to take steps with other newspaper proprietors over the coming months to see if we can collectively improve things", although he was deliberately vague on what exactly might be reformed.