Footage released by BBC Daily Politics shows Mr Mann chasing the former London mayor up the stairs, accusing him of “rewriting history.”
In the footage, Mr Mann is heard shouting: “Go back and check what Hitler did. There’s a book called Mein Kampf.”
Mann’s comments come after Mr Livingstone suggested that Adolf Hitler was a Zionist “before he went mad and starting killing millions of people”, prompting some Labour MP’s to call for his suspension from the party.