The UK wants to rip up the existing Northern Ireland protocol and replace it with new Brexit arrangements, warning it would be a “historic misjudgment” if the EU did not consider such a change.

“What does it cost the EU to put a new protocol in place? It seems to us, very little,” the Brexit minister Lord Frost said in a speech in Portugal on Tuesday.

Spelling out the UK’s position in greater detail than before, he said it was needed if the both sides were to move away from the current hostilities and move to the next chapter.

To allow the current “alienation” to take hold would be “a serious historical error”, he said, adding the UK had got into “a low-equilibrium somewhat fractious relationship” but that “takes two to fix it”.

In a speech recalling the works of philosopher Edmund Burke he questioned why the EU would not want to rewrite the protocol to accommodate the unionist concerns in Northern Ireland.

“It doesn’t seem unreasonable to us to look at an agreement again if it is obviously not doing what it was designed to achieve.

“For the EU now to say the protocol, drawn up in extreme haste, at this time of great uncertainty can never be improved upon when it is so self evidently causing such difficult problems will be historic misjudgment,” he said.

“We always sign treaties and in good faith and intend to implement them. I hope that’s a given.

But he added: “We knew that some aspects of the protocol as it stood when they were agreed in October 2019, we knew that these were problematic. We didn’t particularly support them ourselves. We agreed with them because it was the right thing to do for the country overall,” he said.

It has been a turbulent month for EU-UK relations, with a flurry of speeches, briefings and statements by Lord Frost and Downing Street over the need to substantially rewrite the protocol, signed less than two years ago.

On Monday Ireland’s foreign minister Simon Coveney questioned whether the UK wanted a complete breakdown of relations, saying the EU was close to the point of saying “enough we cannot compromise any more”.

One Whitehall source said the ultimate source of Frost and Boris Johnson‘s unhappiness with the protocol was Theresa May’s decision to accept the EU’s sequencing of negotiations. They said Frost and Boris Johnson were effectively trying to unpick the decision to include Northern Ireland as one of the top three issues in the legally binding withdrawal agreement.

Frost’s speech is the third in a month arguing for the protocol to be changed and the second time he has argued that the original protocol itself allowed for it to be superseded through Article 13 (8). “Given the experience we now have, it is clear that it must,” he said.

Frost insisted he was not abandoning the UK’s international obligations, saying it wanted to use the “grain of the protocol” but “design it in a way that allows goods to flow freely where they need to flow freely and avoid undermining the balance the Good Friday Agreement is designed to establish.”

Frost said the UK would consider the EU’s proposals “seriously, fully and positively”.