LONDON, March 23 -- Thousands of people opposed to Britain's withdrawal from the European Union will march through central London on Saturday to demand a new referendum as the deepening Brexit crisis risked sinking Prime Minister Theresa May's premiership.

After three years of tortuous debate, it is still uncertain how, when or even if Brexit will happen as May tries to plot a way out of the gravest political crisis in at least a generation.

May hinted on Friday that she might not bring her twice-defeated EU divorce deal back to parliament next week, leaving her Brexit strategy in meltdown. The Times and The Daily Telegraph reported that pressure was growing on May to resign.

While the country and its politicians are divided over Brexi...