The union chief said he “couldn’t believe the line of questioning” from the Sky News host as rail workers began the biggest industrial action in a generation on Tuesday morning.
Ms Burley, 61, asked Mr Lynch what the union would do if agency workers hired by the Government attempted to cross a picket line to take up posts left by striking workers.
He responded: “Well we will picket them, what do you think we’ll do? We’re in a picket line and we’ll ask them not to go to work. Do you not know how a picket line works?”
To which Ms Burley replied: “I very much know how a picket line works, I’m much older than I look, Mr Lynch. What will picketing involve.”
Mr Lynch then turns behind to a group of striking workers at Euston Station and says: “You can see what picketing involves. I can’t believe this line of questioning.
“Picketing is standing outside the workplace to try and encourage people who want to go to work, not to go to work. What else do you think it involves?”
Ms Burley went on: “I just wondered what else it might involve because... I very well remember the picket lines of the 1980s”.
She then specifically mentions the miners strikes, which saw strong divides emerge in many communities between workers on pickets and those who crossed them.
Mr Lynch replied: “Well does it look like the miners strike. What are you talking about?
“You seem to have gone off into a world that isn’t real.”
She responds: “I’m sorry that you feel the need to ridicule me, I’m just asking you what you expect your members to do if agency workers…”
Then Mr Lynch interrupts: “Your questions are verging into the nonsense. We run a picket as effectively as we can.”
Many passengers’ journeys took several hours longer than normal during the industrial action on Tuesday, while those who chose to travel by car instead were greeted by a surge in traffic.
Just a fifth of trains ran on Tuesday and half of all lines were closed.