Top U.K. executives are warning Prime Minister David Cameron that he could damage the country's economy by inadvertently taking the country out of the European Union.

In a letter published Wednesday in the Financial Times, Virgin Group's Richard Branson, London Stock Exchange head Chris Gibson-Smith and eight other business leaders are challenging Cameron's plan to renegotiate the U.K.'s membership terms of the 27-country EU and put the matter to a referendum. The executives warn that such a plan could fail, pushing the U.K. out of the EU and hitting business.

Tough economic times are forcing the 17 EU countries that use the euro to move ever closer - creating a more powerful union that could affect how much non-euro members spend - something Britain's leaders are against.