In the meantime, Cameron will renegotiate his country's relationship with the EU to make changes he says will be more favourable, if not to all members, then at least to Britons.

The source of concern is the crisis in the euro-zone.

The relief at having stayed outside the single currency is palpable in Britain. Had it bought in it would have faced problems similar to those plaguing the former "tiger" Ireland.

It is now apparent that if the euro is to survive, and the euro zone remain intact, the EU will have to become more united. This raises the spectre of political union, and the consequent relinquishing of ever more decision-making power to a centralised bureaucracy.

The prospect of a "United States of Europe" plays well to an audience - particularly the British press and right-wing politicians - that likes to play up tabloid reports of "EU directives" supposedly banning straight - or was it bent? - bananas and ordering that the spicy snack formerly known as Bombay Mix should be renamed Mumbai mix.

These myths sit uncomfortably beside concerns about EU encroachment on Britain's sovereign issues, including social and employment laws and measures against crime.

The prime minister remained vague on what changes he wished to make on its membership, citing the EU's notorious red tape. But he spoke of the principles of democracy, sovereignty and British exceptionalism - designed to strike a chord with a sceptical public and enhance his own political credentials.

Until his speech, Cameron had struggled to contain the anti-EU sentiment among his own lawmakers and among right-wing and fringe parties such as the UK Independence Party (Ukip), which campaigned for a clean break.

Ukip has been winning support away from the Conservatives with a noisy campaign against EU membership. It has also lobbied to halt immigration from Eastern European nations, for which membership in the EU guarantees for their citizens the right to live and work in Britain.

Recent polls have shown support for Ukip as high as 16 per cent, compared with 3 per cent during the last election in 2010.

Populist leader Nigel Farage claimed Cameron's referendum announcement was Ukip's "greatest victory to date".

Farage believes that by promising a vote, Cameron has "let the genie out of the bottle" and guaranteed a British exit from the EU "within a few years".

"I see opportunity. We would have the potential to do so much more for this country," Farage said.

Reflecting the general view that Britons have of themselves as players on a world stage, only temporarily stood down from former glories, Farage said that liberation from the EU would see Britain "winning back the right to have global trade agreements - to make us much more of a global player than a European player".

However, it is clear that Cameron does not want Britain to leave the EU. Rather, he wants it to become a "leaner, less bureaucratic union" that co-operates on transnational issues such as terrorism, but leaves the decisions on how a country should be run to the people of that country.

The crux of his message was "more democracy, less bureaucracy", which was long on rhetoric and historical context. It enraged his political opponents by effectively trapping them into having to take an "in-or-out" stand of their own ahead of the next general election.

The Conservatives' partners in the coalition, the Liberal Democrats, are stolidly pro-Europe - but the party's leader, Deputy Prime Minister Nick Clegg, criticised Cameron's pledge as contrary to the national interest and potentially destabilising to its economic recovery.

With the prospect of the economy slipping into an unprecedented triple-dip recession, Clegg said recovery would be stymied by the inevitable wrangling over esoteric issues in the years leading up to the referendum.

Clegg wants Cameron to focus on Britain's economy, but this would be complicated by "years and years of tying yourself up in knots having arcane debates about the precise terms of the membership of the European Union" before a referendum.

"It is not in the national interest when we have this fragile recovery, when we have a very open economy which is very dependent on investors in the car industry and the banking system and so on," he said.

At the risk of alienating supporters, Labour leader Ed Milliband told Parliament that he was not in favour of an "in-or-out" referendum, apparently to the surprise of his fellow MPs.

However, it is a matter of when - not if - Milliband will echo Cameron's referendum call, according to the left-wing , which pointed out the political expediency of such a move on Milliband's part. The magazine said support for an "in-out" referendum" would "fudge internal party divisions", as it has done for Cameron.

Commentators on all sides point out that a referendum would also end, once and for all, the wider doubts about the commitment the British people have to the European Union.

For it seems that no one, least of all Cameron, really believes that the British will vote to leave.

His strategy appears to be based on on the historic reluctance of the electorate to make the constitutional changes that a referendum offers, in favour of sticking with the status quo once the consequences become clear.

In this he may well have stolen a march on his opponents, not least Ukip, by reclaiming the loyalty of the euro-sceptic right wing of his own party.

Polls have already shown a narrowing in support for leaving the EU. A YouGov/ survey last month found 39 per cent of respondents would vote to leave, while 37 per cent would vote to stay. The newspaper noted that those who wanted to leave the EU had a 2 percentage point lead, compared to 21 percentage points a few months ago.

More remarkably - and with more than four years to go - it reported that 50 per cent of those asked said they would vote to stay if Cameron was successful in renegotiating the terms of Britain's relationship with the EU.

By promising to negotiate changes favourable to Britain, Cameron is gambling that he can reclaim sovereignty in some areas, while opting out of further integration.

His speech was undoubtedly aimed at boosting his own and the Conservatives' standing (as public opinion polls show a widening gap in Labour's favour), and appears to have been successful in that regard, at least.

Since his January 23 speech, Cameron - widely derided as an aloof product of privilege in a country still obsessed with class and connections - has been hailed as a statesman of decision and depth. One columnist compared him with Admiral Horatio Nelson, who won the Battle of Trafalgar, and Winston Churchill, who won everything else.

Harvard historian Professor Niall Ferguson said Cameron's words would be remembered by history as "10 times more politically bold" than even those of Margaret Thatcher, who was famously steely in her determination to keep Britain out of the euro zone.

Cameron is also being seen as a risk-taker, depicted on the cover of magazine as a tattooed poker player "unnecessarily" gambling with Britain's fortunes. But, it added, he was playing a stronger hand than many believe, "so, with a bit of luck, his gamble should pay off".

There are early signs that this could well be the case. Alongside the colourful and headline-grabbing hyperbole of a handful of pro-Europe stalwarts, including former prime minister Tony Blair, Cameron appears to have gained support from the leaders of France and Germany.

French President Francois Hollande said he hoped Britain would "remain at the heart of the EU". German Chancellor Angela Merkel said: "One has to find fair compromises. In this context we are ready to talk about Britain's wishes."

Both France and Germany appreciate Britain's EU presence, especially on defence and foreign policy. British logistical support for France in its current Mali campaign is a case in point.

Germany is grateful for British support during the economic crisis and shares Cameron's desire for a deeper single market.

Neither France nor Germany seem particularly in favour of closer political union, or what could for them be costly changes to the euro zone treaty.

Greater flexibility, Cameron believes, will make Europe more competitive in a world increasingly dominated by the developing economies of Asia, Africa and the Middle East.

Since his election in 2010, he has moved Britain closer to India, China, Japan and Australia, seeing wider markets for his country's embattled industries.

But a recent report by Japan's biggest bank, Nomura, pointed to the uncertainty that the referendum announcement has caused, saying it was far from clear that "being freed from EU regulation would be a booster".

"The prospect is, in our view, bound to raise concerns - indeed, is doing so already in the City [London's central business district]," the report said.

The report's author, Alastair Newton, a former British diplomat, predicted a deepening of the euro crisis, which could prompt accelerated integration to prevent a complete collapse of the euro zone. "Attempts to change the terms of the treaty that holds the euro zone together would prompt Britain to demand repatriated powers that the EU could regard as jeopardising the single market," the report said.

This could increase pressure for the referendum to be held sooner rather than later - as Farage demands - and increase the possibility of an "out" call from voters.

Whether Britain opts in or out, both the country and the EU will endure, though somewhat diminished if there is a split. The question for Cameron is whether he will join the list of leaders - Wilson, Thatcher, Major, Blair, Brown - whose careers were shaped by the issue of Europe.

The BBC's Nick Robinson said: "The test of this speech will be whether it makes it easier for David Cameron to live with and survive the issue that has proved more toxic than any other or whether it consumes him as it has his predecessors."