The presenter tried to move to the Remain backing guest as the Brexiteer complained about being repeatedly interrupted.
Ms Burley snapped: “Ladies, come on, it is usually the gents that behave like this. Right, go on, stop it, stop it, go on.”
It comes amid a turbulent week for the Prime Minister after her withdrawal agreement was defeated for a second time on Tuesday evening with a majority of 149 votes, despite obtaining assurances from the European Union.
On Wednesday evening MPs voted to block Britain leaving the European Union without a Brexit deal.
The Government put down a motion for debate on Thursday that offers to seek a one-off extension of Article 50, delaying the scheduled Brexit date of March 29 to June 30 if MPs approve the deal negotiated with the EU by next Wednesday.