British Prime Minister Theresa May has warned MPs in Parliament that failing to back the Brexit deal she agreed with the EU in Brussels would take Britain "back to square one".

May's Brexit deal would be less economically damaging than crashing out of the EU without a deal, according to the first detailed economic analysis published on it, launched on Monday by the People's Vote campaign.

Following a Cabinet meeting on Monday morning to brief ministers on her strategy to sell the deal, May went to the Commons to directly appeal to MPs to "listen" to their constituents and "decide what is in our national interest".

After taking the battle to save her Brexit plan on tour across all four nations of the UK this week, May will head to Argentina for the G20 summit at the weekend.

MPs are expected to vote on the deal in just more than two weeks, with up to 90 of May's own Conservative Party members threatening to rebel against it.

The Brexit secretary, Stephen Barclay, told reporters on Monday that if MPs voted down the deal "we go into uncharted waters".

"This is the best deal, and it's also the only deal, and EU leaders have made that clear," he said.

Barclay conceded it would be difficult to get the deal through Parliament, but said the Cabinet needed to make the case, for it.

"I don't pretend for a minute it's not a challenging task given where the numbers currently look," he said. "But this is a good deal that respects the referendum result.

"And we need to be clear with parliamentary colleagues as to what the alternative will be, which will be massive uncertainty from either no deal or no Brexit."

Labour MP Keir Starmer, the shadow Brexit secretary, said May had "run down the clock" with her Brexit talks, meaning that to renegotiate a better permanent deal would probably require article 50 to be extended beyond March next year.

Starmer argues that if the only alternative was the chaos of no deal, then May and the EU27 would back down and allow this. "If you had a vast majority saying we don't authorise the government to leave with no deal, it would be very difficult politically to do so," he said.

According to the economic analysis revealed on Monday, May's Brexit deal is likely to result in substantial long-term economic costs in a range of 700 to 1,100 pounds ($900 to $1400) per person each year compared with staying in the EU.

Produced by the National Institute of Economic and Social Research (known as NIESR), an independent think-tank, the analysis shows the prime minister's withdrawal agreement is less economically damaging than crashing out of the EU without a deal, but there would be a hit to national income from less trade, foreign investment, productivity and migration.

The NIESR report was launched on Monday by the People's Vote campaign, which funded the study and is pushing for another Brexit referendum.

The findings about the economic impact of the UK leaving the EU are in line with NIESR's work before the 2016 Brexit referendum, which had no external funders, as well as an IMF analysis this month and a government study that was leaked in January.