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The favorites jostling to succeed Theresa May as prime minister are talking up an abrupt exit after almost three years of wrangling

LONDON—In the Brexit lexicon, it is called “no deal.” Forget about negotiating a bilateral withdrawal treaty between the U.K. and the European Union. Just leave and start over.

With Prime Minister Theresa May’s premiership drawing to a close, the specter of a no-deal Brexit once again looms larger. Most lawmakers oppose it. Business executives are terrified of it. But the favorites among those jostling to replace Mrs. May as prime minister are talking up an abrupt exit after almost three years of inconclusive Brexit wrangling.

Britain doesn’t need an agreement to leave the EU; that will now happen on Oct. 31 unless the U.K. takes one of three steps to avoid it. It could agree to a deal, ask the other 27 EU governments for a further delay, or unilaterally decide not to go ahead with Brexit at all.

“No deal has always been the legal default,” said Maddy Thimont Jack, senior researcher at the Institute for Government, a nonpartisan London think tank focused on policy-making.

Ardent Brexit supporters see no deal as the ticket to a bright future free from the long arm of EU regulation. It would mean no finicky negotiations over the Irish border or handing over billions of pounds of taxpayers’ money to settle past commitments to the EU budget.

The U.K. would gain full control of immigration and trade policy and be free to pursue free-trade accords with the U.S. and other countries. Sure, they say, there might be short-term disruption while legal kinks are worked out. But the long-term benefits no deal brings outweigh the risks.

For others, including senior government figures such as Treasury chief Philip Hammond, no deal is to be avoided at all costs. It would mean tariffs on imports and exports to the EU as well as customs and regulatory checks that would hurt U.K. trade.

It would also mean customs checks on the politically sensitive land border between the U.K. and Ireland. Ports set up to handle fast-moving traffic would gum up. Companies such as aerospace giant Airbus SE and car maker Nissan Motor Co. Ltd. have said the disruption to cross-border supply chains from no deal would cripple their U.K. operations. Financial firms and other services providers fear they would lose access to European clients.

A 2018 government study estimated the British economy would be around 8% smaller 15 years after a no-deal exit than it would have been had the U.K. remained a member state. That compares with a shortfall of between 0.6% and 4.9% if it leaves with a Brexit deal, depending on how close a relationship the EU and Britain agreed to keep.

Both sides of the debate recognize that the U.K. and EU would sooner or later have to pick up the pieces after a no-deal exit and find legal agreements on how to manage their future commercial and security relationship. But they differ on which side would gain advantage from dealing with those issues after Britain leaves rather than before.

People who oppose a no-deal exit say the U.K. would have even less leverage afterward than it does now, since the U.K. economy is much more dependent on the EU than vice versa. No dealers think the U.K. relationship is important enough to the EU that its member states will make concessions in the divorce agreement to avoid it.

Meanwhile, some business leaders say the purgatory of repeated Brexit postponements is worse than a no-deal exit.

Jean-Gil Abbate, general manager of Taylors Transport Group, a logistics firm based in England’s East Midlands, said businesses like his would settle for any outcome if it brought the uncertainty over Brexit to an end.

“It’s better if we know now what’s going to happen rather than just postponing it for a better outcome,” he said. “No deal tomorrow is better than a deal in a year.”

No deal appeared to have been banished to the fringes of the Brexit debate once Mrs. May completed her negotiations with Brussels late last year. She twice asked the EU for more time to try to win over rebel lawmakers who repeatedly threw out her Brexit deal, pushing back the Brexit deadline from the original March 29 to Oct. 31 now.

But a Parliament deadlocked over Brexit found a majority for one thing: that the U.K. shouldn’t leave the bloc without a deal.

Now, with Mrs. May saying she will step down, several of those seeking to replace her in Downing Street are putting no deal back in the spotlight—especially since the Brexit Party, which advocates an abrupt split, soundly beat the Conservatives in European Parliament elections.

“There will clearly be a commitment made to no deal on the campaign trail,” said Mujtaba Rahman, managing director for Europe at consulting firm Eurasia Group.

Boris Johnson, the front-runner to succeed Mrs. May, has said a no-deal exit is closest to voters’ vision of Brexit. He said Friday the U.K. should be prepared to walk away Oct. 31 if the EU won’t renegotiate withdrawal.

Dominic Raab, a former Brexit secretary who is also running for the leadership, has said he would opt for no deal if the EU doesn’t drop its demand for an indefinite “backstop” arrangement to prevent the need after Brexit for customs and other checks on the Republic of Ireland’s border with Northern Ireland, part of the U.K.

Having voted before to stop a no-deal exit on March 29, Parliament could try to do it again and tie the hands of a new prime minister. But Ms. Jack said there is no guarantee such an effort would succeed, given the government’s unusual level of control of the legislative process in the U.K.

A bigger constraint is politics. A new Conservative prime minister who, like Mrs. May, lacked a majority in Parliament, couldn’t force through such a profound constitutional change without imperiling the rest of the government’s agenda. Some analysts say there isn’t enough time before Oct. 31 to lay the legal groundwork for a split. Liam Fox, trade secretary, warned over the weekend that no deal risks giving ammunition to advocates of independence in Scotland and Irish unity in Northern Ireland.

Mrs. May’s successor will also have to weigh the risk that a no-deal Brexit opens the door to a greater Conservative bugbear than the EU: Labour Party leader Jeremy Corbyn. Conservative lawmakers fear that if no deal did hurt the economy, they would lose the next election to the veteran left-winger.