Paul Mason, who has held senior positions with the BBC and Channel 4, made the comment during an interview with Sky News presenter Adam Boulton.
He was speaking after it was announced that Jeremy Corbyn had been re-elected as Labour leader, comfortably defeating his challenger, Owen Smith, by securing 61.8 per cent of the vote.
Posting on the social media site Twitter, Mr Mason said: “Should there not be space inside Scottish Labour for those who want Indy?”
He went on to say that he thought the SNP would back a Labour government with a majority in England and Wales.
His comments sparked an angry reaction from some Labour members and supporters.
• READ MORE: Jeremy Corbyn re-elected Labour leader
Also posting on Twitter, Martin McCluskey, who will become Scottish Labour’s political director next month, said: “If Paul Mason believes in party democracy, he should start by listening to @scottishlabour members who don’t want Indy or #indyref2.”
Labour MSP Neil Findlay said: “I think I need to have a pint with Mr Mason to advise him he’s talking bollocks.”
However, former Labour Party member Denise Couper tweeted support.
She said: “It is Scottish Labour’s only hope, unionists are going to the Tories. Scotland’s choice - either Indy in EU or Westminster Tory rule.”
Paul Mason is one of Britain’s best-known journalists. He was culture and digital editor of Channel 4 News, becoming the programme’s economics editor, a post he formerly held on BBC2’s Newsnight programme.
He has written several books, including Postcapitalism and Live Working Or Die Fighting.