LONDON — British Prime Minister Theresa May made a frantic last push Monday to swing lawmakers’ support behind her seemingly doomed Brexit deal, warning that its defeat risked scuttling the U.K.’s departure from the European Union and “betraying the vote of the British people.”

May claimed to have gotten reassurances with “legal force” on key issues from the EU, and said history books would judge Parliament harshly if lawmakers did not back Britain’s orderly exit from the EU when they vote on the agreement Tuesday.

“Over these next 24 hours, give this deal a second look,” May implored skeptical lawmakers in the House of Commons.

May said rejecting her deal would lead either to a reversal of Brexit — overturning voters’ decision in a 2016 referendum — or to Britain leaving the bloc without a deal, a course that would damage the country’s economy, security and unity.