British Prime Minister Rishi Sunak won the overwhelming backing of parliament on Wednesday for a key element of the deal despite opposition from Northern Ireland's Democratic Unionist Party's (DUP) small number of lawmakers and some of his party.

The DUP has said it will not drop a year-long boycott of Northern Ireland's devolved assembly without "further clarification, re-working and change" to the Windsor Framework agreed last month by the United Kingdom and the European Union last month.

"That deal is done. There is no renegotiating of that deal," Chris Heaton-Harris told reporters in Belfast after meeting Northern Ireland's main parties.

"I will always talk to every single member of Northern Irish political parties but the time for negotiation on the Windsor Framework is over."

The DUP, at odds with an opinion poll this week suggesting 45% of Northern Irish voters support the framework versus 17% opposed, has raised concerns over the continued role of EU law and Northern Ireland's place in the UK's internal market.

As part of Britain's departure from the EU, British-run Northern Ireland effectively remained in the bloc's single market to avoid a hard border with EU-member Ireland.

Negotiators feared such a border could have endangered a 1998 peace deal which largely ended three decades of armed conflict in Northern Ireland. An internal trade border with the rest of the UK has instead angered many pro-British unionists.

DUP leader Jeffrey Donaldson has said his party might yet be convinced to support the new deal in the future if additional concessions are made.

"I am not interested in sticking plasters, they don't work and I'm afraid there is an element of the sticking plaster in the Windsor Framework," Donaldson told reporters on Thursday.

"When the prime minister has the time, we will be sitting down with him and we'll be putting forward our case ... I'm not a quitter, I've never given up in terms of seeking to achieve what we need to achieve."