Mr Livingstone, who quit Labour in May, did so saying issues around his suspension for alleged antisemitism had become a distraction.
At the time he told the JC: "This has dragged on for two years now. I’ve had lies and smears just repeated and repeated. I’m 73 next month; I don’t know how long I’m going to be around for..."
He quit the party just before a disciplinary hearing into his repeated claims that Hitler was "supporting Zionism before he went mad and ended up killing six million Jews”.
Mr Livingstone said he did not regret the remarks.
Attacking Mr Johnson in an interview with LBC on Friday, Mr Livingstone said: “We’ve had a real increase in Islamophobic incidents, very often a woman wearing a burka gets it ripped off their face. Boris is pandering to that fear of Islam and bigotry.
“We all know Boris one day is going to try and become the next leader of the Tory party and if he’s going to be trying to mobilise bigots in the Tory Party behind him, that’s totally wrong.
“Again and again, he will say things that are completely wrong. He isn’t really a politician, he just wants to be a famous celebrity. He doesn’t do the detailed work, he doesn’t get on top of issues. It’s just one-off remarks all the time and frankly I think the Tory Party should dump him.”
Mr Livingstone, whom Mr Johnson beat in the 2008 election, added: “If he ever became a Prime Minister, he would be a disaster for Britain.
“He was mayor of London for eight years, what did he do in that time? He built a cable car to nowhere, which is a huge loss of money. And the ArcelorMittal revolving thing overlooking the Olympic site.
“He just sat there for eight years promoting himself.”
Mr Livingstone's row over Hitler and zionism lasted two years, during which he was suspended from the party, until he resigned in May without any formal rebuke or conclusion about his remarks.
Jewish communal groups condemned the resignation, with JLC chair Jonathan Goldstein Mr Livingstone had apparently "taken one for the team” and that his resignation would allow him to continue to stand on official Labour Party platforms to campaign “without the issue of antisemitism being properly determined”.
