Now it is centre stage again, and the debates between Eurosceptic Nigel Farage and Europhile Nick Clegg bring the argument down to a stark, binary choice not seriously faced in decades - In, or Out.
But why does Europe produce such a polarised reaction? Many Britons, on both sides of the debate, love visiting European countries and idolise elements of their culture - not least the food. Indeed, more than 1.5 million Britons have moved there to live.
But Europeans viewing British newspaper coverage, political debates or opinion polls would be forgiven for thinking we have little but contempt for our neighbours. It is, to say the least, a complex relationship.
The weight of history
Maybe it is the long history of hostilities that clouds the British view of Europe with suspicion. As an empire builder and major trading power it was inevitable that Britain would come into conflict with rivals vying for the same territories and trade routes. And allegiances shifted. All of its main rivals - Germany in the world wars, Russia in the Cold War, and France through most of modern history - have also at times been important allies.
But for many historians the most enduring influence on Britain's self-image is World War Two. And it may be that the popular perception of Britain in its Darkest Hour, standing alone as the British Empire against Nazi Germany in 1940-41, informs a modern view of the UK as its own best friend. And that if anyone can be relied on to come to her aid, it is the United States.
Britain, obviously, is an island nation. Is this the key to its arms-length attitude to Europe? For centuries "we lived in splendid isolation, protected by the Navy and the Empire", the historian Vernon Bogdanor has said. "Now, of course, that period of isolation has long gone, but perhaps it still retains some of its impact upon the British people, who do not want ties with the Continent."
But other members of the EU - Ireland, Malta, and Cyprus - are islands, and they do not object so much to handing powers to Brussels. Perhaps it is Britain's island mentality, combined with that imperial hangover, that is at play - Britain is used to giving orders, not taking them.
An end to war
The formation of the European Union had its origins after 1945, in the desire to tie Europe's nations so closely together that they could never again wreak such damage on each other. Winston Churchill fully supported this idea, proposing for Europe "a structure under which it can dwell in peace, in safety and in freedom... a kind of United States of Europe".
But as the European Coal and Steel Community was forged in 1951, Britain stood on the sidelines; and it declined an invitation to join the six founding nations of the European Economic Community in signing the Treaty of Rome in 1957.
One of the architects of the ECSC, Frenchman Jean Monnet, said: "I never understood why the British did not join. I came to the conclusion that it must have been because it was the price of victory - the illusion that you could maintain what you had, without change."
Britain wants in
With its own economy stuck in a rut, Britain saw France and Germany posting a strong post-war recovery and forming a powerful alliance, and changed its mind. It applied to join the EEC in 1961, only for entry to be vetoed - twice - by French President Charles de Gaulle. He accused Britain of a "deep-seated hostility" towards European construction, and of being more interested in links with the US.
Britain may have had selfish reasons for wanting to sign up, but then seeking mutual benefits is part of the motivation for the European project. As the historian James Ellison points out, Europe has not just been a place of conflict for Britain over the centuries. "It was also a place of diplomatic agreement, trade, co-operation and - through most of the second half of the 20th Century and the 21st - peace and stability and growth," he says.
Britain gets in
Conservative Prime Minister Edward Heath finally led Britain into the EEC in 1973, after Gen de Gaulle had left office. When membership was put to a referendum in 1975, it had the support of Britain's three main parties and all its national newspapers. The result was resounding - with more than 67% voting in favour. But that did not end the debate. There was no immediate economic fillip - in fact strikes and power cuts continued, and rising oil prices caused double-digit inflation.
Role reversal
Margaret Thatcher campaigned for EEC membership in 1975
In the 1970s, the Conservatives backed British membership - though there was some opposition on the right of the party. The most concerted opposition came from the left of the Labour party, led by Tony Benn and Michael Foot. Mr Foot's 1983 Labour manifesto promised withdrawal from the EEC - by then more commonly called the European Community (EC) - after the pro-Europe wing of the party had split off to form the SDP.
"Europe has been a toxic issue in British politics," Prof Bogdanor says, not just because it caused division between parties, "but also deep divisions within the parties".
"Some might argue that the fundamental conflict in post-war British politics is not so much between left and right as between those who believe that Britain's future lies with Europe and those who believe it does not."
Rising antipathy
In 1984, Margaret Thatcher corrected what was seen as an injustice, negotiating a permanent rebate for Britain on its EC contributions, because it received much less in agricultural subsidies than some other countries, notably France.
The 1980s saw a growing divide between Britain and Brussels, where the socialist Jacques Delors had taken the helm at the European Commission and was steering towards a more federal Europe and a single currency.
Mrs Thatcher was uncompromising. Her 1988 speech in Bruges, in which she rejected "a European super-state exercising a new dominance from Brussels", has become a seminal text for Eurosceptics. But, with many Europhiles in her cabinet (far more than nowadays), her stance fuelled the Conservatives' internal warfare, and helped lead eventually to her downfall.
Humiliation
"Black Wednesday" was one of the lowest points in Britain's relationship with Europe. After failing to fend off intense currency speculation, Chancellor of the Exchequer Norman Lamont was forced to announce Britain's withdrawal from the Exchange Rate Mechanism on 16 September, 1992.
1992 and all that
Mrs Thatcher had been unable to stop Europe's march towards political union, and was gone by the time the Maastricht Treaty was signed by her successor John Major in 1992. This involved huge transfers of power to the new European Union. Britain secured opt-outs from the single currency and the social chapter. But to the treaty's critics - including many Tory rebels - it undermined the British tradition of the inviolable sovereignty of parliament.
Building bridges...
A pro-European Tony Blair was well received in Europe - until the Iraq war
Tony Blair followed a landslide election victory in 1997 by quickly patching things up with Europe. He signed Britain up to the social chapter, delivering some of the social protections long coveted on the left, and setting his sights on the euro. But Britain's economy was doing well, support for euro entry was not widespread, and Chancellor Gordon Brown put the plans on hold.
…and burning them?
David Cameron became the first British PM to block a new European treaty
The euro crisis has put paid to any prospect of Britain adopting the single currency, and has perhaps fuelled the Euroscepticism that now apparently runs strongly through parts of the Conservative Party and the public at large.
In December 2011, as EU leaders tried to tackle their problems through a treaty setting new budget rules, David Cameron demanded exemptions and then vetoed the pact. To critics, this cut Britain adrift. But it delighted Eurosceptics and encouraged them to demand more. Soon enough, the prime minister promised a referendum on British membership. Britain's most poisonous political issue was back centre stage.
1 April 2014 Last updated at 00:14 GMThttp://www.bbc.com/news/uk-politics-26515129