Former public health minister Steve Brine asked Julia Hartley-Brewer to tell him "the point of Brexit" during a heated debate on the breakfast show.
The discussion kicked off after host Julia said the "whole point" of leaving the EU was to leaving the single market and customs union to make "our own free trade deals".
However, Conservative MP Mr Brine said that was simply her "opinion".
"Well, what was the point of Brexit? Other than those things?" Julia asked.
"You tell me!", Mr Brine responded.
He continued: "The Prime Minister has had to decipher what 17.4 million meant when they voted Leave. What she did was come up with a brilliant compromise across 27 member states, which did honour everything in the manifesto."
The politician resigned from the government last week in order to support Sir Oliver Letwin's amendment to hold a series of "indicative votes" on alternative Brexit options.
MPs are set to vote again today on a number of alternatives, which will be decided by Speaker John Bercow.