The former EDL leader was challenged by the councillor as he continues his campaign for the European election in May.
In a video posted on Twitter on Monday, Freddie Bailey, a Labour councillor from Preston, confronted 'Tommy Robinson' in Blackpool, where Robinson had been campaigning for the upcoming European Parliamentary elections.
Robinson, whose real name is Stephen Yaxley-Lennon made headlines this week when he had a milkshake poured over him by members of the public two days in a row.
Bailey, who was re-elected to his seat in the Garrison ward on Friday, said that he decided to travel to Blackpool to meet Robinson because he "wanted to ask him if he thought he was racist."
In the tweet, Bailey said "Today in Blackpool I met 'Tommy Robinson' and his far right supporters. Some did threaten and square up to me but no milkshakes were thrown. I will appose (sic) anyone who tries to create divisions in our society."
In the video, which Bailey filmed himself, he stands next to Robinson and says: "Can I ask, do you think you're racist?" to which Robinson asks: "For talking about a religion?"
The pair, who were surrounded by a crowd, then debated the meaning of the term "Islamophobia".
The video has since been viewed over 100,000 times on Twitter.
"Everyone knows the definition of a racist," Bailey said, "a person who discriminates against people of other races."
"Tommy Robinson believes Muslims are all enemies of the state as he has said many times. He has tried to stir up hate in our community and turn people against one another when we should all live cohesively and love one another."
Asked whether it was better to ignore far right figures than give them attention online, Bailey said, "You can't ignore hate because it grows. You have to stand up to it and face it head on and argue against their opinions. That way we will win the argument and people like Tommy Robinson realise they are part of the problem why society is so divided."