The BBC presenter repeatedly asked what evidence there was to suggest Whittingdale had effectively blocked the second part of the Leveson inquiry to please newspapers, and prevent them printing details about his private life that surfaced late last night.
But Evan Harris, a former Liberal Democrat MP and executive director for Hacked Off, failed four times to provide proof for the claims, and eventually admitted he might be wrong.
Appearing on the 'Daily Politics' programme, Neil asked why Whittingdale's refusal to order a new inquiry into press ethics was to placate newspapers hostile to potentially greater regulation so they would keep his story quiet.
Responding, Harris said of the culture secretary: "In a recent meeting I said: 'Why have you taken the power to decide whether sign into law, this thing that parliament passed?' He said it will keep the press on their toes.
"Now it's not the job of a secretary of state to keep the press on their toes.
"Until they give an alternative reason why the government decided to intervene in press regulation ... there is no other reason why he would be doing that if there wasn't a suspicion that he wanted to please the editors to stop them publishing."
Asked by Neil if he was claiming Whittingdale had acted to block another press inquiry because he knew journalists were looking at his story, Harris said "there doesn't seem to be any other explanation".
The two clashed again when Harris claimed Whittingdale would have told David Cameron about his relationship with a dominatrix, when he was first appointed as culture secretary, if he was not trying to curry favour with editors.
Neil blasted the 'Hacked Off' campaigner's lack of proof, asking: "You don't know whether, when he was appointed cabinet minister, that he knew the newspapers were looking for this story do you?"
Harris insisted it was a question for Whittingdale himself to answer, before Neil hit back and said: "But you were the one who made the claim that he should have told the Prime Minister when he was a cabinet minister.
"What I'm asking you is did he know there were investigations going on and you now tell me you don't know?"
Harris admitted in response: "If it isn't the case then his position is much better, 'cos if he didn't know they had a story, how could he be influencing him?"
Commentators described it as a "car crash" interview.
Whittingdale came under scrutiny last night after details of his relationship with an escort surfaced. Four newspapers, the People, Mail on Sunday, the Sun and the Independent, all learned about it, the BBC reported, but decided it was not a public interest story and spiked it.
In a statement today, John Whittingdale insisted he had not been influenced in his role as culture secretary by newspapers' knowledge of the dominatrix, known as 'Mistress Kate'.
“Between August 2013 and February 2014, I had a relationship with someone who I first met through Match.com. She was a similar age and lived close to me,” he said.
“At no time did she give me any indication of her real occupation and I only discovered this when I was made aware that someone was trying to sell a story about me to tabloid newspapers. As soon as I discovered, I ended the relationship.
“This is an old story which was a bit embarrassing at the time. The events occurred long before I took up my present position and it has never had any influence on the decisions I have made as Culture Secretary.”