Europe is gearing up for a summer of discontent. There’s the British referendum on European Union membership, a simmering refugee crisis and an increasingly desperate European Central Bank.

Taken together, this list gives reason enough to be fearful about the health of the European project in the coming months.

But there is also Greece, which is caught in a spat between Germany and the International Monetary Fund over debt relief as it seeks yet more bailout money.

Greece, whose economic crisis already threatened to destroy the irrevocable nature of euro membership, still seems to be dragging its feet over state asset sales and pension reform. It is haemorrhaging cash from its banking system. Athens has to find more than €5 billion (about $5.7 billion) to meet its debts in June and another €€5 billion in July. That’s€€10 billion that Greece doesn’t have; not, perhaps, a princely sum for a larger, healthier European state, but 20 per cent of Greece’s annual tax income. Now, there’s an argument that with so much else going on in the European theatre, Brussels will be keen to fudge a solution just to get Greece off the agenda. The IMF may not be so willing to oblige, however. If May comes and goes without a deal, be it because of German intransigence on debt relief, IMF stubbornness on budget targets or Greek brinkmanship, Greece and its creditors may run out of time to avoid default.

As Greece’s debt repayment deadlines approach, EU officials may be busy fighting fires kindled by Britain’s June 23 referendum on EU membership. The outcome of that vote is far from certain. Bloomberg’s composite tracker of opinion polls puts votes to remain in the EU at 39 points, those wanting to leave at 38, with “don’t knows” holding the balance of power at 23.

With Prime Minister David Cameron embroiled in a domestic row about his personal taxes in the wake of the so-called Panama Papers, government popularity is likely to take a hit. That can only help the anti-EU campaign; it will not take many undecided voters to swing the outcome.

The European Commission’s regular survey of attitudes to the EU, known as the “eurobarometer”, has already taken a turn for the worse, with the most recent poll showing rising discontent:

“The proportion of Europeans for whom the EU conjures up a negative image has risen to 23 per cent (+4); before this, it had declined continuously in the four previous surveys.”

Renewed concern about the European project is just starting to surface in the bond market.

Investors are now charging Portugal 3.3 percentage points more for ten-year money than they demand from Germany, a spread that is well above its six-month average of 2.2 points. Italy’s risk premium rose to 1.3 points last week, up from December’s low of 0.9 points, while Spain is at 1.4 points, up from 1.2 points a month ago.

That is not enough to ring alarm bells, but it is odd at a time when the ECB is increasing its sovereign bond purchases.

While last week’s Dutch rejection of a treaty between the EU and Ukraine hinged on a very low turnout about a very specific policy, it does hint at the disquiet rumbling through the EU.

A British decision to quit may prompt other countries to hold ballots on their own membership — Marine Le Pen has already promised referendums as part of her campaign strategy for the 2017 French presidential elections.

So the timing could turn out to be disastrous. The IMF, which says Greece cannot turn itself around without debt relief, may be unable to reconcile its differences with Germany, which says further relief is irrelevant to a solution. The EU may find itself trying to hand money over to its weakest and most begrudging member just when one of Europe’s most important participants, if the Brexit vote goes against the British Government, has called it quits. Instead of hitting the beach this summer, Europe’s leaders may find themselves trying to stop their sandcastle from crumbling.

•Mark Gilbert, the author of Complicit: How Greed and Collusion Made the Credit Crisis Unstoppable, is a Bloomberg View columnist and a member of the Bloomberg View editorial board.