The timing could hardly be worse, as the EU struggles with its biggest migration crisis since World War II and the continent facing a growing threat from terrorism fuelled by conflict in the Middle East.
Analysts said any such division within the bloc would likely be seized upon by Russia, whose ties with the EU have been badly damaged by the Ukraine conflict.
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The EU has been keen to increase its influence around the world in recent years.
The bloc helped negotiate the landmark nuclear accord with Iran, and has worked closely with Washington and Moscow in an effort to revive stalled peace talks between Israel and the Palestinians.
Analysts said losing a UN Security Council permanent member and Nato lynchpin like Britain would likely diminish the EU's influence and respect around the world, while also making it more inward-looking.
"It would be bad news with a view to the role of the EU. It would increase the loss of image if the EU shrinks for the first time in its history," Janis Emmanouilidis, director of studies at European Policy Centre, told AFP.
"The signal would be that the EU gets slowly but steadily in a downward trend," he said, suggesting that such weakness could be exploited.
"The Chinese and the Russians might use that... To exert pressure and divide further."
Pertusot said there would also be a loss of influence in areas such as Latin America and Southeast Asia which regard the EU as a model for regional groupings such as Mercosur and ASEAN.
The prospect of a British exit has raised the possibility in some quarters that it would free up the bloc to move ahead on its own in forging a more united global position.
But analysts say there is no appetite for that, adding that most member states look to US-led NATO for security when push comes to shove in a crisis. Of the EU's 28 member states, 22 are members of the military alliance.
Rosa Balfour at the German Marshall Fund of the United States said a Brexit would effectively wreck efforts to forge what the EU now calls its Common Security and Defence Policy (CSDP).
"As a major security and military provider in Europe, a British exit... Is likely to have a disastrous effect on the EU's CSDP," Balfour told AFP.
"Without British assets, it is questionable whether it is worth pursuing defence integration.
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