Former Brexit Minister David Jones | Rosie Hallam/Getty Images Continued EU court oversight means no Brexit, says former UK minister Former Brexit Minister David Jones admitted that the failure to get a deal in Brussels on Monday had been a ‘difficult day.’

If the U.K. does not leave the jurisdiction of the European Court of Justice, it will not have left the European Union, former Brexit Minister David Jones said Tuesday.

Admitting that Theresa May's failure to secure a deal in Brussels Monday on a path to sufficient progress in the Brexit talks was a "difficult day", Jones indicated that there may be more difficulties for the British prime minister at home than just the Northern Irish border sticking point. May's parliamentary partners, the Democratic Unionist Party (DUP), torpedoed the deal that was all but done in Brussels over the issue of so-called "regulatory alignment" on either side of the border.

But Jones said there were other problems to be ironed out. "The European Court of Justice is effectively the supreme body within the European Union," Jones told BBC's Today program. "If we are continuing to be subject to its jurisdiction, then again we have not in reality left the European Union."

He said that he would need "more detail" on the proposal though and so would not "dismiss it out of hand."

Jones, who supported the Leave campaign in the Brexit referendum, said he was "pretty sure there will be people in Downing Street who will regret it not making the position clear with the DUP and ensuring everything was agreed before they actually got on the plane to Brussels." He said that "there should have been more clarity," adding that "the prime minister has got a lot of talking to do to Arlene Foster [DUP leader] today."

Lord Peter Ricketts, former permanent secretary at the Foreign Office, told the program that the visit had been "damaging for the prime minister."

"If we are to make a success out of Brexit, indeed if we are to have Brexit at all, we've got to make sure that we are free to conduct our own trade arrangements the way we want to," Jones said. "If we maintain a regulatory alignment with the European Union then that makes it extremely difficult if not impossible," adding that he did not favor such a regulatory alignment.