* Europeans question benefits of integration -Pew Research
* But majority say they want to keep the euro, survey shows
By Robin Emmott
BRUSSELS, May 29 (Reuters) - Support for European integration has fallen sharply across the European Union since the public debt crisis began, but few Europeans want to abandon the euro and stricken Greeks are keenest to keep the common currency, a study showed on Tuesday.
A growing number of Europeans in Britain, France, Spain, Italy, the Czech Republic, Poland and Greece say integration has weakened their economies and question whether membership of the European Union is a good thing, according to a report by the non-profit, Washington-based Pew Research Centre.
The study aims to provide a greater insight into attitudes and trends in Europe and has been taken into account previously by U.S. officials when formulating policies towards the continent.
Only in Germany, Europe's largest economy and biggest contributor to the bailout programmes supporting indebted Ireland, Greece and Portugal, has enthusiasm for the EU grown since 2009. Sixty-five percent of Germans see membership in a positive light, up 2 percent from a Pew poll in 2009.
Yet even as 54 percent of Spaniards doubt the value of being in the European Union - a huge political and economic project created in the aftermath of World War Two - the fall in support does not translate into calls to ditch the euro currency.
Despite enduring the country's second economic recession in just three years, 60 percent of Spaniards still support the common currency, highlighting the tensions and contradictions of a bloc guided by a founding philosophy of "ever closer union."
In Greece, where a rejection of the EU/IMF-mandated austerity programmes by voters earlier this month has intensified concerns that the country may leave the euro, just 23 percent of the population want to return to the drachma.
"The irony here is that people who have the euro still want to keep it," said Bruce Stokes, director of Pew's global economic attitudes project in Washington.
"People realise that it would be a leap into the dark to go back to their old currencies," he said.
A desire to drop the euro appeared to be strongest in Italy, with 40 percent of those polled saying they wanted to return to the lira, but with a majority in favour of the common currency.
In Britain, where the question of European economic and political union have divided the country and toppled prime ministers for more than half a century, 73 percent of people polled said being out of the euro was a good thing.
Many economists and academics say the euro, which was introduced to Europeans in coin and note form on January 1, 2002, is flawed because it lacks the structural underpinning to make it work as a common currency across 17 economies.
Given the lack of an obvious alternative to the euro, EU leaders agreed at a summit in Brussels this month to look at ways to deepen integration across the euro zone and possibly move towards a fiscal union to complement monetary union.
For its study, Pew polled about 1,000 people in each of the surveyed countries in the euro zone - Germany, France, Italy, Spain and Greece - as well as in non-euro zone Britain, Poland and the Czech Republic.
The survey was carried out between mid-March to mid-April and the margin of error was three to four percentage points.