Julia Hartley-Brewer and Tom Brake clashed over Brexit terminology on the breakfast show.
The Liberal Democrat Brexit spokesman used the term "crashing out" to describe a no-deal Brexit, whilst discussing an online petition calling for Article 50 to be revoked, which has garnered millions of signatures.
"I guess the reason signatures were secured in such large numbers is because up until yesterday, there was a real prospect of crashing out of the EU," he said.
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Julia interjected: "Can we use the correct terminology? Leaving the EU. There's no crashing out."
"In what way is leaving the EU on WTO terms three years after we voted to do so crashing out?. This phrase seems to be allowed to be used on a daily basis and it has no meaning."
Mr Brake argued that the term reflected what would happen in the event of a no-deal, saying there were "some things we would want to avoid", including losing access to the EU arrest warrant.
"You think the EU police forces and UK police and security services would suddenly decide 'Let's not bother helping each other out'?" Julia asked.
"If that's the best example you can come up with I don't think there's anything to be scared of."