The upper chamber of Parliament inflicted another embarrassing defeat this week on the government of U.K. Prime Minister Theresa May, challenging her plan to leave the European Union's single market and her government's fixed timing for Brexit.

May, who has struggled to unite the government behind her vision of Brexit, has said the U.K. would also leave the European Union's single market and customs union after it quits the bloc next March.

That stance has widened divisions not only within her own Conservative Party but also across both houses of Parliament, which — like Britons at large — remain deeply split over the best way to leave the EU after more than four decades of membership.