Carried out as part of the EU's 'Eurobarometer' survey, the poll asked whether British citizens supported the idea of "a constitution for the European Union".
Contrary to the results of previous polls on the issue, where a majority of those questioned had voiced opposition to an EU constitution, the new poll suggests a 49% to 29% backing for the idea.
The pollsters stressed that the poll does not refer directly to the proposed EU Constitution, and so cannot be taken as an indicator of voting intention in the forthcoming referendum. However, the result is sure to raise eyebrows in both Yes and No camps.
Fiona Hall, Liberal Democrat MEP for the North East, commented:
"This poll suggests that the British public is perfectly able to accept the idea of a written constitution for the EU.
"Now the battle has to begin to persuade them of the merits of this particular Constitution, which has been accepted by the European Parliament and all member state governments after very thorough negotiations.
"Those who want Europe to punch its weight in world affairs and who want parliamentary democracy to work at the European level, will all vote Yes.
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