In private conversations with executives of some of the U.K.’s biggest firms, Prime Minister David Cameron’s advisers have urged executives to set the tone of the debate early, according to a government official familiar with the strategy. In the Scottish referendum in 2014, many businesses kept quiet until the last minute for fears of alienating customers who disagreed with their stance.

“The business community will be more vocal and organized” than it was then, said the chief executive of a large British company familiar with Downing Street’s plans. He added the prime minister’s office has been liaising with companies over strategy for at least several months. Mr. Cameron on Saturday said a referendum on whether the U.K. should remain within or leave the union would take place June 23, officially kicking off the campaign.

Downing Street’s guidance to industry has included advice on how to cast the message, including voicing support for a “reformed” EU, according to a lobbyist, a tack that echoes the prime minister’s position.

The group of about 200 companies voicing their support spans a wide variety of sectors, from financial services to pharmaceuticals and retail. A key part of Mr. Cameron’s campaign to convince the British public to remain in the EU rests on the argument that the U.K. would be better off economically.

The companies announced their support in a letter published in the Times of London on Monday night that includes signatures from chief executives at companies including Rio Tinto PLC, HSBC Holdings PLC, AstraZeneca PLC, Royal Dutch Shell PLC and Goldman Sachs International. They said leaving the EU “would deter investment, threaten jobs and put the economy at risk.”

Among the companies on the list is Airbus Group UK. Paul Kahn, head of Airbus’s U.K. operations and president of the industry’s trade body ADS Group, speaking before the letter was published, said “remaining part of the EU is the most effective way to shape and influence regulation.” He said membership allows businesses access to integrated European supply chains with minimal red tape and to European investment in research and development. Almost 90% of the trade group’s members export to the EU, he said.

Also on the list is energy company Centrica PLC. Its CEO, Iain Conn, said the U.K. has more influence over European energy policy as part of the club and, as a major gas importer, would benefit from the increased competitiveness of a common energy market.

“Just speaking as an energy guy, that’s why from that narrow lens I believe we should be better off in than out,” he said.

But certain companies, including some of Britain’s supermarkets, have shied away from entering the debate, insisting the matter is one for customers to decide.

One of the groups campaigning for Britain’s exit, called Leave.EU, said the prime minister was applying pressure to chairmen and executives. It also said a number of companies say Britain’s departure from the EU would make no difference to their job count or investment plans in the U.K.

In a speech to Parliament on Monday, the prime minister said uncertainty over Britain’s intentions toward the bloc could hurt working people for years. “When it comes to people’s jobs, it is simply not enough to say that it will be all right on the night and we will work it out,” he said.

Mr. Cameron also mocked the idea—put forward by some so-called euroskeptics including London mayor and fellow Conservative politician Boris Johnson—that Britain could vote to leave and then have a second negotiation with the EU. Mr. Johnson delivered a blow to the prime minister Sunday when he announced his opposition to staying in the EU.

Those lobbying for Britain to leave the EU argue business would be better off without what they consider to be interference from Brussels in how British business operates. Mr. Johnson, the most high-profile figure in the pro-exit camp, said Monday the economic risks of leaving the EU are overblown and that those best placed to understand the needs of U.K. business and industry are in London, not Brussels.

Many businesses support Britain’s continued membership of the EU, though some, particularly smaller ones, express frustration with what they consider to be cumbersome red tape. Many say the risks of leaving outweigh the benefits, according to Andy Bagnall, director of campaigns at the Confederation of British Industry, an organization representing U.K. businesses.