MacKenzie, who was editor of the paper at the time of the notorious "The Truth" article, last week gave his profuse apology for the story, which blamed Liverpool fans for the 1989 disaster.
The Sun also apologised for the article and issued a new story entitled "The Real Truth".
However, Thomson confronted MacKenzie over key new revelations about his handling of the article.
In a Channel 4 News report, Thomson starts by attempting to talk to MacKenzie through the door of his house, asking him for an "interview on camera".
After MacKenzie refuses to come out, Thomson presses him through the shut door on recent statements made by Harry Arnold, who wrote the original article.
Speaking on a BBC documentary, Arnold said that he had written the story in a "fair and balanced way", stressing that the controversial claims of "mass drunkenness" and criminal behaviour among the Liverpool fans were said to be just "allegations".
He said that MacKenzie had applied the headline "The Truth", and then dismissed Arnold's objections to the way the story was being presented.
Unable to get a response, Thompson later approaches MacKenzie as he attempts to get into his car. At one stage, the ex-tabloid editor tries to drive away with Thomson still half inside the vehicle.
"Don't assault me, don't assault me," Thomson warns as MacKenzie reaches for the door handle.
MacKenzie states in the film that he intends to talk about the situation "next week".
"It's not up to you to decide whether I answer questions," he says. "I will do it next week."
Asked about what he would say to the people of Liverpool, the former tabloid editor adds: "I have already said how sorry I am."
But when he accuses Thomson of being "not reasonable", the Channel 4 News presenter counters: "That's pretty rich coming from you. I think the public are going to love that, Kelvin."