The British would vote to quit by 51 per cent to 49 per cent if an in-or-out referendum were held now, the Express reported earlier.
It was the second poll in a month to show a majority want to leave after decades of support for continuing to stay in.
And the result will step up calls for a referendum on membership to be held sooner rather than later.
The pan-European survey also found growing disenchantment with Brussels across the Continent – including Germany and France.