By Chris Bowlby
Reporter, Radio 4's Analysis
Up to 55% of those asked in recent British opinion polls say they would support it. But it's hardly ever discussed in polite political society. What is this great taboo?
Britain leaving the European Union.
Plenty of people in the UK still want a referendum on the Lisbon treaty
After all the constitutional wrangling and embarrassing referendum results within the EU in recent years, reluctance to talk about this among the EU mainstream may be greater than ever.
But look carefully at the focus of all that wrangling, the Lisbon Treaty.
It contains a shock for those used to the EU talking of "ever-closer union".
Buried deep in the treaty is a kind of anti-integration time-bomb, a clause which sets out clearly for the first time how an EU member state could "withdraw from the Union in accordance with its own constitutional requirements".
British Labour MP Gisela Stuart is at least partly responsible.
She is not, herself, in favour of the UK leaving the EU.
But she insisted on such a clause going in when she helped draft the European constitution, the forerunner of what is now the treaty.
"Most of my colleagues", she says, thought this was "heresy
bit like going into a marriage contract where you have at the bottom: PS Should this not work, I may consider divorce".
But some on the continent, privately at least, now think the current UK-EU relationship might need to end.
Leaving the EU would come at a price, officials warn
"Certain people are beginning to ask themselves - so is it worth it?" says Marco Incerti, from the right-leaning Centre for European Policy Studies.
They would be "more prepared than in the past to accept a divorce", he believes.
But what would a divorce between Britain and the EU mean in practice?
It's hard to know precisely. Like any such separation, much would depend on the mood in which it was done, co-operative or acrimonious.
Legally, a key moment would be a decision at Westminster to repeal the 1972 Act which paved the way for the UK joining what was then the European Communities.
But as the EU is a treaty organisation, all sides accept that a deal would also have to be done on how the UK withdraws from its EU commitments, and what kind of new relationship with Europe is established.
The UK Independence Party peer Lord Pearson is confident that the rest of the EU will feel co-operative.
"They'd be delighted to get rid of us", he predicts.
Price of withdrawal
Sir Stephen Wall, once the UK's top official in Brussels and adviser on Europe to Tony Blair, agrees that other EU countries "would certainly want to do a deal", especially for continued access to British markets.
But he warns that they would also want "to make us pay a price just as the French made us pay a huge price for joining in the first place".
So Britain could end up continuing to pay into the EU budget for some time as part of a deal.
Ireland's Yes vote turned the corner for supporters of the treaty
Lord Pearson, keen to stress the savings he believes would come from a UK exit, says that UKIP wants "to continue in friendly free trade and therefore we will phase out what we send
over an agreed period".
Others warn of a more disruptive split over trade.
Simon Hix, professor at the London School of Economics, suggests that cheap flights to EU countries could be threatened if new costs were imposed on British airlines.
He sees a potential threat too to what's available in British shops such as French wine and Italian cheeses.
This "cuisine culture" has happened "because of the European single market," he says. "Do we really want to give that up?"
Such claims are dismissed by Daniel Hannan, the Conservative MEP whose support for a UK referendum on the Lisbon Treaty led him to quit his frontbench position earlier this month.
"This is the great myth - that if something isn't regulated by Brussels there would be no collaboration whatever," he says.
There are many other intriguing aspects of a UK exit.
How would Scottish opinion respond? How would the transition in farming and fisheries work, as the UK extricated itself from common EU policies?
Also, what would happen to the residence and working rights of EU citizens in Britain, and British citizens abroad?
Sir Stephen Wall, who is very keen on the UK remaining in the EU, concedes that in economic terms, the consequences of leaving should not be exaggerated. "Catastrophe it isn't," he says.
But, in the end, he would expect a major loss of British influence with the UK no longer being part of the EU block.
"There is no alternative way of advancing the British national interest," he says. In trade negotiations for example "the Americans play hard ball
you have to have the strength to hit them hard where it hurts in response. On our own, it's quite difficult for us to do that".
If people did vote to leave, he feels, a few years later they "might turn round and say why did nobody tell us what the consequences were".
The current reluctance of mainstream politics to talk about these scenarios flies in the face of British opinion poll results suggesting a strong - even a majority - interest in leaving the EU if a close relationship can be maintained with Europe.
"You can't swim for ever against the current of public opinion", argues Daniel Hannan.
Britain leaving the EU would be an unpredictable process.
But the idea that all this is simply inconceivable and irrelevant is no longer credible.
Analysis: Divorcing Europe will be broadcast on BBC Radio 4 on Monday 16 November 2009 at 2030 GMT and repeated on Sunday 22 November at 2130 GMT. Or download the free