The former Conservative Prime Minister had urged ministers to consider the risks of a no-deal scenario for the UK, particularly on matters related to security.
Mrs May told the Commons: “The Government appears resigned to the prospect of no deal, yet one area which they should not be resigned to the prospect of no deal is in security.”
The MP for Maidenhead said neither Mr Gove nor Boris Johnson had mentioned security in recent statements, adding: “Will [Mr Gove] confirm that if the UK walks away with no-deal then our police and law enforcement agencies will no longer have the necessary access to databases, such as PNR (Passenger Name Record), in order to continue to identify and catch criminals and potential terrorists in order to keep us safe?”
Mr Gove said “significant progress” has been made over security co-operation, adding: “But it is the case that the EU are insisting that before we have access to systems, like the Schengen Information System, we have to accept the jurisdiction of the European Court of Justice – we cannot accept that.”
Mrs May reacted with shocked expressions. She repeatedly said “what?” in disbelief and appeared to mouth “utter rubbish” as Mr Gove continued.
He said: “The second thing I’d say is there are many, many areas in which we can co-operate more effectively to safeguard our borders outside the European Union than we ever could inside, through a variety of methods and arrangements open to us, open to Border Force and open to our security and intelligence services – we can intensify the security that we give to the British people.
“The third thing I’d say to [Mrs May] is that I agree with her: when it comes to everything, security and other matters, no deal is better than a bad deal.”
It comes after Mr Gove claimed the EU was refusing to intensify talks in order to reach a trade deal agreement.
The Cabinet Office Minister said that the Prime Minister and European commission president Ursula von der Leyen had agreed on October 3 that their teams would work “intensively” to bridge the remaining gaps.
He told MPs: “We made clear that we were willing to talk every day. But I have to report to the house that this intensification was not forthcoming.
“The EU was only willing to conduct negotiations on fewer than half the days available and would not engage on all of the outstanding issues.
“Moreover, the EU refused to discuss legal texts in any area as it has done since the summer. Indeed it’s almost incredible to our negotiators we have reached this point in the negotiations without any common legal texts of any kind.”
His comments came after the EU’s chief negotiator Mr Barnier tweeted: “I just spoke to [Lord Frost]. As stated by President [Ursula von der Leyen] on Friday, I confirmed that the EU remains available to intensify talks in London this week, on all subjects, and based on legal texts. We now wait for the UK’s reaction.”