The former prime minister was caught on camera looking at a colleague in astonishment and asking “what?!” as Gove made the comments during a Commons statement.
He was answering May, who raised concerns that a failure to agree a deal with the EU before the end of the transition period on December 31 could hamstring the police and intelligence services’ ability to catch criminals and potential terrorists.
Gove said staying in EU crime databases would mean ongoing European Court of Justice jurisdiction in the UK, which he said would be unacceptable.
And the Cabinet Office minister even threw back one of May’s old maxims when she was PM by insisting “no deal is better than a bad deal”, even on security.
The two have long been enemies, dating back to the so-called Trojan horse affair when a briefing war erupted between Gove’s Department for Education and May’s Home Office, which was accused of failing to “drain the swamp” of extremism.
When May became PM in 2016, she sacked Gove before reinstating him to the cabinet a year later as environment secretary.
But the pair’s clash in the Commons showed the old tensions have not completely eased.
During Gove’s statement, May asked: “The government appears resigned to the prospect of no deal yet one area in which they should not be resigned to the prospect of no deal is in security.
“I note that my right honourable friend made no mention of security in his statement this afternoon and the prime minister made no reference to security in his letter to parliamentarians on October 16.
“So will my right honourable friend confirm that if the UK walks away with no deal then our police and other law enforcement agencies will no longer have the necessary access to databases such as PNR in order to be able to continue to identify and catch criminals and potential terrorists in order to keep us safe?”
Gove replied: “The first thing to say is that significant progress has been made in respect of security cooperation but it is the case that the EU are insisting that before we have access to systems like the Schengen Information System 2 (SIS 2), that we have to accept the jurisdiction of the European Court of Justice.
“We cannot accept that.
“The second thing I would say is that there are many, many areas in which we can cooperate 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 and security services, we can intensify the security that we give to the British people.
“And the third thing I would say to the right honourable lady is that I agree with her – when it comes to everything, security and other matters, no deal is better than a bad deal.”