LONDON — After two crushing defeats in Parliament for her plan for Britain’s withdrawal from the European Union, Prime Minister Theresa May nonetheless had high hopes of cajoling or threatening enough recalcitrant lawmakers to win approval in a third try this week.

On Monday, though, the speaker of the House of Commons, John Bercow, stood in her way — again.

His weapon? An 1844 guide to parliamentary procedure that relies on rules dating back to 1604.

Mr. Bercow told the government that Parliament could not vote a third time on its plan for Brexit, as the departure from the European Union is known, unless the plan substantially differed from the one rejected last week.

As the speaker, Mr. Bercow, who is officially nonpartisan, determines whether or not critical votes are taken in Parliament. And he has angered the government by using this power, it says, to try to influence the Brexit process.