The tense Brexit exchange came after Theresa May gave a monumental speech outlining her future plans for the UK’s negotiations.
The Prime Minister called for a bold and creative agreement to be reached with the European Union, insisting “Britain’s future is bright” outside the bloc.
She also set out a new immigration system, which will be implemented during the two-year transitional phase as the UK quits the EU.
Speaking in Florence, Mrs May said: “During the implementation period people will be able to live and work in the UK but there will be a registration system.”
She added it would be an “important building block” to “taking full control of our borders”.
BBC political editor Laura Kuenssberg, asking a question after the Prime Minister’s Florence speech, suggested there would be voters in the UK who may be disappointed by her points on immigration and market rules.
Kunessberg added: “The European courts will have a role, potentially until 2021 – five years after the referendum – aren’t they justified about being a bit cross about that?
“And, is no deal better still better than a bad deal?”
The Prime Minister instantly fired back, insisting she had set out an “entire speech about what a great deal we can have”.
She added: “I’ve set out how we can do that today, and achieve a deal that I believe is not just in the best interests of UK citizens but of people remaining across the remaining 27 states.”
On the issue of immigration, Mrs May responded: “People voted to leave the EU, and at the end of March 2019 we will leave the European Union.
“But I think people also voted to ensure that process of leaving could be orderly and smooth so people had confidence in their future and businesses had confidence.
“That’s what I’ve set out today, an implementation period which provides for that smooth and orderly withdrawal.
“There will be a difference during that period because we will be asking EU citizens who come to the UK, they will be able to do so, but we will be asking them to register – that’s an important building block towards the full set of immigration rules.
“That’s an important stage of us taking full control of our borders.”