Top UK executives have warned Prime Minister David Cameron that he could damage Britain's economy by inadvertently taking the country out of the European Union.

The businessmen made the warning in a letter published today in the Financial Times.

Among the group were Virgin Group's Richard Branson, London Stock Exchange head Chris Gibson-Smith and WPP chief executive Martin Sorrell.

They and seven other business leaders challenged Cameron's plan to renegotiate the UK'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 UK out of the EU and hurting business.

EU membership offers access to the common European market, facilitating trade, and a role in negotiating the future of the continent's financial policies. Britain has also benefited from EU funds to build infrastructure such as broadband networks.

Though the business leaders urged EU reform, they argued "we must be very careful not to call for a wholesale renegotiation of our EU membership, which would almost certainly be rejected."

"To call for such a move in these circumstances would be to put our membership of the EU at risk and create damaging uncertainty for British business, which are the last things the prime minister would want to do," they cautioned.

Tough economic times are forcing the 17 EU countries that use the euro to move ever closer, creating a more powerful union that could leave non-euro members like Britain with less negotiating power.

But while Cameron wants Britain to retain influence in the EU, he is also resisting a push by many member states, like France and Germany, to grant central authorities in Brussels greater powers over financial and legal affairs for the whole of the EU.

In the long run, many EU countries want to turn the bloc into a United States of Europe, an idea British politicians, particularly among Cameron's Conservatives, are totally against.

Cameron is due to make a speech in mid-January to outline his position and the requests he will make. He told UK lawmakers today that Britain could get the changes it wanted.

"We're active players in the European Union but there are changes we would like in our relationship that would be good for Britain and good for Europe and I think because of the changes in euro zone which is driving a lot of change in the European Union there's every opportunity to achieve that settlement and seek consent for it," he said.

Distrust in Britain over the EU has grown in recent years as the bloc struggled to effectively combat a financial crisis affecting the region's 17-member euro zone.