Britain's opposition Labour Party will vote this week to keep a second Brexit referendum on the table if Theresa May fails to pass her plan to quit the European Union through parliament, heaping pressure on a struggling prime minister.

After May's plans for Brexit — the biggest shift in British policy for more than four decades — were rebuffed by the EU on Thursday, the outcome of talks to leave are more uncertain than ever and have boosted those who want to stop the divorce.

Labour leader Jeremy Corbyn has been reluctant to support behind growing demands for a second referendum, or People's Vote, but the motion agreed by members after more than five hours of debate may satisfy both sides of the party's divide.