Conservative Prime Minister Theresa May will open five days of debate on the deal she has agreed for Britain to withdraw from the European Union on Tuesday, as she faces widespread opposition ahead of a planned vote by lawmakers next week.

May is scheduled to speak at the start of the debate. She has promised parliament a "meaningful vote" on the agreement that EU leaders endorsed for Britain to leave the bloc after 40 years.

"Our duty as a parliament over these coming weeks is to examine this deal in detail, to debate it respectfully, to listen to our constituents and decide what is in our national interest," May told lawmakers earlier.

"We can back this deal... Or this house can choose to reject this deal and go back to square one," she said.

Most opposition lawmakers have dismissed May's public campaign to rally support for her deal, while many Conservative eurosceptics also oppose it.

Several dozen Conservatives have vowed to vote against the deal on December 11, while Northern Ireland's Democratic Unionist Party, whose 10 lawmakers prop up May's minority government, also opposes it.

The DUP and many Conservative eurosceptics are angered by May's acceptance of a temporary backstop to guarantee an open Irish border after Brexit.

The backstop could place Northern Ireland under slightly different, indefinite arrangements from the rest of the United Kingdom.