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Dominic Cummings was one of architects of the 2016 campaign to leave the European Union.Alastair Grant/The Associated Press

Members of Parliament will be unable to stop a no-deal Brexit on Oct. 31 by bringing down Britain’s government in a vote of no-confidence next month, Prime Minister Boris Johnson’s top aide has advised, according to The Sunday Telegraph.

Dominic Cummings, one of architects of the 2016 campaign to leave the European Union, told government ministers that Mr. Johnson could schedule a general election after the Oct. 31 Brexit deadline if he loses a vote of no-confidence in Parliament, the newspaper said, citing sources.

“[MPs] don’t realize that if there is a no-confidence vote in September or October, we’ll call an election for after the 31st and leave anyway,” Mr. Cummings was quoted by one of The Sunday Telegraph’s sources as saying.

A top official of the opposition Labour party strongly disagreed.

“There will be opportunities for us when Parliament returns in September to stop no deal,” Labour’s Jon Ashworth told Sky News.

“The government will have to bring forward appropriate legislation to prepare for this Brexit no-deal exit that they want. And we will use all the means available to us in Parliament ... and we will work to stop no deal.”

Labour has said it will oppose any Brexit deal brought forward by Mr. Johnson if it does not protect jobs, workers rights and the environment.

Mr. Johnson has promised to lead Britain out of the EU on Oct. 31 with or without a deal but has a working majority of just one after his Conservative Party lost a parliamentary seat on Friday.

Some of his MPs have hinted they would vote against him to prevent a no-deal Brexit — a rising prospect that has sent the pound tumbling to 30-month lows against the U.S. dollar over the last few days.

Parliamentarians are unable to table a motion of no confidence before next month because the House of Commons is in recess until Sept. 3.

Mr. Johnson has said he would prefer to the leave the EU with a deal but has rejected the Irish backstop — an insurance policy to prevent the return of a hard border between the Irish Republic and Northern Ireland — which the EU says is key to any agreement.

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