The warning comes as new polls suggest a rise in Euroscepticism across Europe.
A survey by Ipsos Mori suggests 58 per cent of Italians and 55 per cent of the French want a referendum on the EU, and that 48 per cent Italians would like to even bid farewell to the EU.
In a new analysis on the impact of Britain exiting the EU, Guy de Jonquieres, of the European Centre for International Political Economy (ECIPE), says, "The EU needs to overcome wider public disaffection with and mistrust of, not just EU institutions, but establishment politics at national level as well.
"A similar popular mood is spreading across much of the rest of Europe. A UK vote for Brexit would strengthen the growing populist and nationalist forces in the EU that want their countries to leave it and even to dismantle the European Project altogether," adds de Jonquieres, a former Financial Times journalist and senior fellow at ECIPE.
"What makes that challenge so powerful is that Europe's leaders, under rising pressure from insurgent parties at home, have few ideas about how to respond to them."
In a publication, 'The UK Referendum and the Future of the European Project,' he says, "There are fundamental problems at the heart of the 'European Project.' But there is a serious shortage of realistic solutions, still less a political consensus on what they should be."
Meanwhile, a new poll published on Friday has found that 51 per cent of Scots support remaining in the EU compared to 21 cent who support leaving, a bigger margin for Remain than the UK as a whole.
However, despite the Scottish government's argument that Scotland being taken out of the EU 'against its will' would be grounds for a second independence referendum, the poll also found that 46 per cent disagreed, with 43 per cent in favour.
Elsewhere, the UK Labour party set out new analysis on Friday showing what a "Tory Brexit budget" would look like if the UK were to leave the EU on 23 June.
Labour says the hit to the UK economy caused by leaving the EU would weaken the public finances and "leave a Tory government committed to austerity being forced to set out how they would meet their discredited fiscal targets."
Labour's analysis of figures from the Institute for Fiscal Studies shows that a "Tory Brexit Budget" will hit public services and family finances "hard."
Tom Watson, Labour's deputy leader, said, "Austerity is a political choice, not an economic necessity. If the UK was to vote to leave the EU we know the Tories would choose more austerity to deal with the economic fall-out and meet their discredited fiscal promises.
"Leave campaigners like Boris Johnson and Michael Gove need to tell the British public what a Tory Brexit would mean in terms of the public finances and further austerity."