Prime Minister Theresa May was set to hail "a new sense of optimism" in Brexit talks on Monday, telling Parliament Britain and the European Union should sign off on a deal at a summit this week "to move forward together" to discuss future trade ties.

May, weakened after losing her Conservatives' parliamentary majority at a June election, emerged triumphant last week after rescuing an agreement to move the negotiations to unravel more than 40 years of union on to their second phase.

But the discussion of Britain's trade relationship with the EU after Brexit contains many pitfalls and could widen differences among her top team of ministers, or Cabinet, over how Britain should look after it leaves the bloc.