Stephen Doughty, a member of pro-EU campaign group Open Britain, was grilled by LBC host Andrew Castle over his Brexit stance.
Mr Doughty, Labour MP for Cardiff South and Penarth, argued Britain should stay in the single market and the customs union.
The pro-European MP also said people are entitled to change their mind and should be given the right to do so with a second referendum.
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Mr Castle said: “You're in favour of staying in the Customs Union, staying a part of the single market, paying the price for that in terms of the immigration, the freedom of movement, take in rulings from the European Court of Justice and everything else.
“I mean there's a new phrase isn't there - BRINO - that's what you're actually aiming for. We're not going to be leaving at all if you have your way.”
The Labour MP rejected Castle’s claim and argued it was possible to place a “series of restrictions” on freedom of movement inside the single market.
BRINO - that's what you're actually aiming for. We're not going to be leaving at all if you have your way
He said: “You wouldn't walk into a car showroom blindfolded and just get into a car and drive off and find yourself falling off a cliff.
“Similarly if you bought a car and you suddenly discovered it had wonky steering and didn't do as many miles to the gallon as you thought it was going to do you you'd ask for a refund.”
Mr Doughty was not the only one to claim people should be given the right to vote again at the end of the Brexit negotiations.
Former Prime Minister Tony Blair has also been campaigning for a second Brexit referendum.
The former Labour leader said people did not have a clear understanding of the implication of the June 2016 Referendum.
Like Mr Doughty, Mr Blair claimed people “have the right to change their mind” on Brexit.
