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* UK business: Britain must be at heart of a reformed Europe
* Wholesale changes to UK's role in Europe would be dangerous
* David Cameron set to give important EU policy speech
By Peter Griffiths and Brenda Goh
LONDON, Jan 9 (Reuters) - Prime Minister David Cameron will damage Britain's fragile economy if he demands major changes that could threaten the country's relationship with the European Union, business leaders said on Wednesday.
In an open letter, the heads of some of Britain's biggest companies said Britain can't afford to quit a market of 500 million people that buys half of its exports.
Other countries in the 27-nation bloc would probably reject Cameron's attempts to claw back powers from Brussels, isolating the country from its biggest trading partner, they said.
"We must be very careful not to call for a wholesale renegotiation of our EU membership, which would almost certainly be rejected," they wrote in a letter to the Financial Times.
"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."
But asked in parliament about Britain's EU role, Cameron repeated his pledge to renegotiate its position.
"There are changes we would like in our relationship that would be good for Britain and good for Europe," Cameron said. He is due to give a long-delayed speech setting out his European policy in mid-January, his spokesman has told reporters.
The rising popularity of the anti-EU UK Independence Party has fuelled talk of a British exit. UKIP leader Nigel Farage said the open letter was a "desperate attempt" by business leaders "to keep their privileged positions", protected from competition by EU regulations.
Trailing in the polls before an election due in 2015, Cameron is under pressure from within his ruling Conservative Party to reclaim powers from Brussels or promise a public vote on Britain's EU membership.
Britain joined the EU's predecessor in 1973, but has stayed out of Europe's single currency zone.
The business leaders said leaving the EU after 40 often turbulent years would damage exports of financial, legal and accounting services. Financial services and insurance make up about 10 percent of Britain's economy, as does manufacturing.
Leaving would raise the cost of exporting and exclude Britain from shaping EU rules, they said, urging Cameron to push instead for EU budget reforms and changes to employment law and to rules governing energy, telecoms and digital services.
Among the signatories were Chris Gibson-Smith, chairman of the London Stock Exchange ; Roger Carr, president of the Confederation of British Industry lobby group; Jan du Plessis, chairman of Rio Tinto Plc and Martin Sorrell, chairman of BT Group Plc.
The letter said trading with the EU from outside the bloc - like Switzerland and Norway - would penalise UK companies and mean Britain could miss out on the benefits of a possible future EU free trade deal with the United States.
Around 25 billion pounds ($40 billion) of Britain's annual tax revenues could be lost because they come from activity that could easily be moved out of Britain, they said.
Cameron's coalition partners, the pro-EU Liberal Democrats - have criticised his stance, while the opposition Labour Party, which has had its share of divisions over Europe and campaigned for Britain's exit in the 1980s, said Cameron was risking Britain's influence abroad to appease elements in his party.
Former prime minister Tony Blair has said a British exit would be a "monumental error". Peter Mandelson, a former Blair minister and ex-European Commissioner, called it "economic insanity".