But what if it's a choice between a single country called Europe or a splintered continent?
Mr. Cameron is determined to avoid that scary scenario.
A day after he shook up Europe's political landscape by offering British citizens the prospect of a vote on whether to stay in the 27-country European Union, Cameron insisted Thursday he wants Britain to remain a part of the bloc but that more unification would not be the answer.
In an interview with The Associated Press afterward, Cameron insisted said he wanted to make Europe "more open, competitive, flexible — so that we can secure Britain's place within it." "I think it is eminently achievable," he said.
Many in the EU, particularly among the 17 countries that use the euro, are on a drive for closer political unification, and that's raised particular concerns recently in Britain, which has often viewed the bloc through a business prism.
"If you mean that Europe has to be a political union, a country called Europe, then I disagree," said Cameron.
On Wednesday, Cameron put an end to months of speculation by revealing he intends to hold a referendum on Britain's membership of the EU, if he wins the next general election, expected in 2015. But many politicians in Europe think closer political ties are exactly what is needed to maintain continental unity in the face of a debt crisis that's laid bare fundamental flaws in the euro.
The European Union, which last year won the Nobel Peace Prize, effectively started amid the rubble of World War II — the motivation to avoid future wars. Some even think Europe's end-game has to be to resemble the United States of America.Countries would be so tied together in their economic and social fabric to make war inconceivable.
After decades of bit-by-bit integration, the links are now so tight that many European leaders refuse to publicly acknowledge that a British exit is a possibility. Several accuse Cameron of putting the bloc at risk to deal with domestic political problems. His Conservative Party has a hardcore element that is highly skeptical of the EU, while an anti-EU party, the UK Independence Party, is gaining ground in the polls most notably at the expense of Cameron's Conservatives.
Italian Premier Mario Monti said Britain should set aside ideology and look at its membership in the EU with "pragmatism, which should be a British attitude of mind."
He argued that Britons, for all their hostility to EU regulations and bureaucracy, benefit so much from the single market that they would be scared to leave — a ready access to markets and over half a billion people would be a gamble too far.
Most of British business appears to want to stay in the EU but out of the integrationist drive — but the question is whether that can be achieved.
"The vast majority of businesses across the UK want to stay in the single market, but on the basis of a revised relationship ... that promotes trade and competitiveness," said John Langworth of the British Chambers of Commerce.
He was among 56 British business leaders who issued a public letter to the Times of London on Thursday complaining about demands from Brussels and calling for "a more competitive, flexible and prosperous European Union that would bring more jobs and growth for all member states."
Growth is certainly something that Europe is craving. The eurozone as a whole is in recession and figures Friday are expected to show the British economy, the EU's third-largest, halfway back to its third recession in four years.
Open Europe, a London-based think tank, says that 48 percent of the UK's goods and services exports are to the EU. The single market keeps down the cost for Britons of doing business with the EU as well as the price of goods imported from the EU for purchase by ordinary British citizens. Membership gives British citizens the right to live and work anywhere in the EU — unlike citizens of other countries, who must seek complicated and often hard-to-get residency and work permits.
Mark Gray, a spokesman for the EU, said the bloc affects almost all aspects of the lives of Britons, from the quality of the water they swim in at beaches or in pools, to the quality of the orange juice they have for breakfast and the conditions in the offices where they work.
But many Britons — like citizens elsewhere in the EU — see the union as a faceless beast imposing rules and spending on needless things and threatening sovereignty.
Britain's relations with Europe have been strained since the end of World War II. It did not join the European Steel and Coal Community, the forebear of what would later become the European Union, in 1951. Britain later realized there were benefits accruing from joining up with some of its wartime friends and foes, and joined the evolving European bloc in the 1970s. It has stood against many efforts to forge closer ties, notably the creation of the euro, but was at the forefront of the drive to create a single market.
Don Melvin in Brussels and Martin Benedyk in Davos, Switzerland, contributed to this report.