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Earlier, Labour leader Jeremy Corbyn said he would back a second Brexit referendum if his Labour Party voted to pursue the move, heaping pressure on May, whose plans for a divorce deal with the EU have hit an impasse.
He also said he preferred a new election to a new referendum on Brexit, reluctant to back growing demands to support a "People's Vote" on Britain's decision to quit the EU for fear of losing those Labour members who voted to leave.
Britain is to exit the EU in March next year. But little is clear after May's plans for Brexit - the biggest shift in British policy for more than four decades - were resoundingly rebuffed by the EU on Thursday, with any outcome of the negotiations more uncertain than ever.
With talk of a new election swirling and chances of a disorderly departure that could damage the economy rising, the opposition party is under pressure to set the Brexit agenda.
But it is not clear how far the new motion will take a party that has said for some time has said that a second referendum is not off the table.