Yet this one involved Mr Clifford himself, when yesterday's Kilroy debate on BBC1 on the allegations surrounding the Tory MP Jerry Hayes became a little more heated than expected.
According to a spokesman for Kilroy Television, Mr Clifford, who publicised the allegations about a relationship between Mr Hayes and a young male researcher, and the Conservative MP Roger Gale began "staring each other out" before the programme began.
"All of a sudden Max lunged forward from his seat and sat right in front of Roger. They were nose to nose snarling at each other. We tried to intervene and then Derek Hatton said to Max, 'If you want a scrap, scrap me'," he said. "When Derek jumped in he accidentally nudged Boris Johnson of the Daily Telegraph and some water went over Margaret Hodge. There was a melee. Max threw his arms out and accidentally caught Annabel [Heseltine] on the arm. This was happening minutes before we went on air. Everybody thought it was going to be cancelled."
The programme, described as "somewhat heated", went ahead, with a BBC spokesman commenting, "It always gets quite frisky".
Last night Mr Clifford, who recently announced a personal vendetta against the Government, and Mr Gale were still at loggerheads, over who started the altercation.
"I am told that he said that if I was in the same studio he would hit me" Mr Gale said. "I was astonished by his behaviour, which appeared to be to try to physically intimidate me.
"But I am not the easiest person in the world to be intimidated. I have been critical of him in the past and shall continue to be in the future. He has certainly got an attitude problem and he does not like Tory MPs."
Mr Clifford denied trying to punch anyone. He said he crossed the studio to confront Mr Gale when he spotted the MP mouthing words at him. "He was either blowing me kisses or saying something," he said. "I don't think he was blowing me kisses. I've told him before I think he's utterly repulsive. There's no love lost between us."
Mr Hatton, not generally known for his mediation skills, said of his role: "I always step in to make sure peace and tranquillity are around. I just wanted to make sure everything was friendly."Reuse content