LONDON—For months, many executives across Britain PLC—and their peers on the other side of the English Channel—held out hope that the U.K.’s eventual withdrawal from the European Union somehow could preserve their membership in Europe’s tariff-free, “single market.”

The government of Prime Minister Theresa May has long signaled it might not. On Tuesday, she cleared up any doubt and said it wouldn’t, sending companies and trade bodies searching for something to take its place—and fast.

Some of the most vulnerable industries to an eliminated single-market membership: financial markets, auto makers and aerospace. All of these sectors have benefited from free and easy access to customers and products on both sides of the Channel.

An official Brexit is still as much as two years away, and the government hasn’t said much about how it will negotiate a replacement deal with Europe.

“It is essential that there are transitional arrangements in place to avoid disrupting closely integrated supply chains,” Paul Everitt, head of Britain’s aerospace trade group, said following Mrs. May’s comments.

Alastair Brown, chief executive of Lombard Risk, a risk-management consultancy in London, warned of a “minefield” ahead for U.K. firms trying to navigate new regulatory and compliance requirements across multiple international markets amid Brexit negotiations.

Many smaller British businesses backed the June 23 Brexit vote, expecting a U.K. unfettered from Brussels would thrive. Most large multinationals preferred the certainty of remaining inside the European Union. A big reason was the tariff-free access to Europe’s giant market.

Mrs. May said she would pursue instead an ambitious new trade deal with the EU, but she provided few specifics. Any deal would be far from the current, zero-tariff arrangement with Europe. In a worst-case scenario, if Britain weren’t able to hammer out a deal, European trading partners could revert to off-the-shelf tariff rates drawn up by the World Trade Organization.

Mike Hawes, chief executive of the SMMT British automotive industry trade group, said maintaining free trade with the bloc would “not be easy.”

Mrs. May also said for the first time Tuesday that a final Brexit deal would be subject to a vote by parliament, a concession that sent the British pound sharply higher.

Specifically abandoning the single market also cleared up at least one issue upon which U.K. business leaders had sought clarity.

“Today’s speech has confirmed what many believed was coming—that the U.K.’s opening position is for a clean Brexit,” said Jessica Gladstone, partner and international law specialist at Clifford Chance. She said businesses could now begin making preparations for the consequences.

One company that said it wasn’t too fussed: Diageo PLC, the world’s biggest maker of Scotch. Even without an agreement, default WTO tariffs for the export of many alcoholic beverages are zero.

“Regardless of the U.K.’s deal on Brexit, U.K. spirits products will continue to enter the EU tariff-free,” said a spokeswoman for the U.K.-based liquor giant. “Our priority is to work with the U.K. government, trade bodies and others to negotiate the best deals to grow our business, and U.K. exports, around the world.”