British Prime Minister Theresa May convened her cabinet and was to face parliament on the newly-agreed Brexit deal on Monday, as she begins the tricky task of selling the plan to a sceptical country.

May returns to a mutinous parliament after sealing the agreement with European Union leaders at a summit in Brussels, where both sides insisted the divorce deal was the best and only option available.

But she faces a big battle to win MPs’ approval ahead of a vote next month, with politicians from all parties, including many of her Conservative colleagues, opposed.

“We can back this deal, deliver on the vote of the referendum and move on to building a brighter future … Or this house can choose to reject this deal and go back to square one.

“It would open the door to more division and more uncertainty, with all the risks that will entail,” she is to warn politicians, according to advance excerpts released by her Downing Street office.

The agreement, which was sealed on Sunday, prepares for Britain’s smooth exit from the EU on March 29, 2019, and sets out a vision for “as close as possible a partnership” afterwards.

It covers financial matters, citizens’ rights, provisions to keep open the UK’s land border with Ireland and arrangements for a 21-month post-Brexit transition phase.

The lengthy, legally enforceable divorce deal is accompanied by a short political declaration setting out hopes for future ties, including security, trade and migration.

May will now embark on an intensive nationwide campaign to promote it — and the risks of no-deal — ahead of a vote by politicians on or around December 12, according to reports.

However, the disparate anti-deal forces are readying for a fight, including the Labour main opposition.

Its Brexit spokesman Keir Starmer told BBC radio that if parliament rejected the deal, May would either have to renegotiate or hold a general election.

The government was to hold a special briefing on the Brexit deal for Labour MPs — an unusual but not unprecedented move.

Arch-Brexiteers despise the agreement, arguing it keeps Britain too closely aligned with the bloc.

Conservative former foreign secretary Boris Johnson branded the deal a “disaster” and a “humiliation” for Britain.

“We are a satellite state — a memento mori fixed on the walls of Brussels as a ghastly gaping warning to all who try to escape,” the Leave campaign figurehead wrote in The Daily Telegraph newspaper.

Irish Prime Minister Leo Varadkar said European leaders were not speculating on alternatives to the deal.

“We don’t want to give the wrong impression to people, whether they are passionate Remainers or passionate Brexiteers, that there is another agreement that can command the support of 28 member states. There isn’t.

“It’s this deal or a no deal scenario,” he said.

In early afternoon deals, the pound edged up against the euro and dollar, while London’s benchmark FTSE 100 index of leading share prices was up 0.7 per cent.

Meanwhile a report by the independent National Institute of Economic and Social Research found that trade with the EU, especially in services, was likely to be more costly after Brexit and have an adverse effect on living standards.

“GDP in the longer term will be around four per cent lower than it would have been had the UK stayed in the EU,” the report said, a loss equalt to around £1000 ($A1770) per year per person.

Newspapers were split on whether to accept the deal, walk away or seek a new referendum.

The Sun said it was “not a diplomatic compromise. It is a surrender”.

Mrs May today begins her frantic two-week race to convince the British public, and a skeptical Parliament, to back the Brexit deal she has struck with the EU and plans to address legislators in the House of Commons later in the day.

British parliament is set to vote on Mrs May’s deal on December 11.