Jess Phillips claimed business chiefs were "going to make Poland great again" by shifting British business over to the Continent.
However, it remained uncertain how Britain will continue its relationship with the customs union, which allows goods to cross borders without customs checks.
Andrew Neil shot down Jess Phillips' claim that businesses would flee post-Brexit Britain
Where are these car plants going to come from that are going to Poland?
Ms Phillips responded: "No, they are just going to say we will take the car manufacturing that currently exists where I live and we’re going to put it in Poland – to make Poland great again!"
But Neil was less than convinced by her argument and decided to take her to task over her statement.
He blasted: “Where are these car plants going to come from that are going to Poland?
“From where? They’re going to move Jaguar to Poland?
The Nissan car plant in Sunderland was said to be at risk last year
“They’re going to move Nissan to Poland?”
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Given her chance to reply Ms Phillips, MP for Birmingham Yardley, which is located close to Jaguar’s UK plant in Solihull, accused Mrs May of wanting to introduce extra “red tape” to the economy.
“It’s like the Conservatives are arguing for red tape – which is so weird,” she added.
Last October Nissan announced it would build its next Qashqai and X-Trail models at its Sunderland plant.
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Continued cooperation with the EU to tackle terrorism and international crime.
The move safeguarded over 7,000 jobs but Business Secretary Greg Clark was criticised in some quarters for allegedly giving the car giant preferential treatment.
After hints from Mr Portillo the EU was using this as “retribution” against Britain, Polish politician Radoslaw Sikorski, who was also appearing on show, claimed the bloc was not to blame for the complexities.
He said: “The European Union doesn’t have to do anything. Britain will put itself outside the customs area – that means the external tariff will apply without the EU doing anything.
“You’re resigning from the club and you’ll be treated as a member of the public.”
He also laughed off claims from Chancellor Philip Hammond that Britain will become a European “tax haven” if it isn’t given off sufficient access to EU markets, he concluded: “You can lower your corporation tax without leaving the European Union.”