Leaders of other EU countries are unlikely to make the same mistake of letting their populations vote on the issue.
Hint: it's by a similar mechanism to referendums
Same way as the structure of the EU itself is decided. Governments fight to keep things away from a vote. Regularly a vote is called anyway because some politician uses the promise of a vote as a way to get elected. Then the EU loses the referendum, election, ... that is called, and then the result is ignored.
https://en.wikipedia.org/wiki/Referendums_related_to_the_Eur...
Direct quote from Wolfgang Schauble (according to Yanis Varoufakis) : "elections cannot be allowed to set economic policy for the EU".
That sums up the attitude of the EU, and is the attitude that permeates both the EU itself and the basis of it's support. This is a quote from a private conversation I had with a Dutch judge. "What would have happened if we had let elections decide ? Norway would be driving on the left and we wouldn't have the Euro anywhere". The EU is seen by the local elites (the non-businessmen. Lawyers, teachers, doctors, ...) as a way to impose what they consider good policy.
The EU institutions itself are importantly not the real basis of power in the EU. Politicians get sent off to the EU to have a cushy, but faraway, job. It's where political careers go to die (especially the parliament). EU politicians are perceived to have less power than the local ones, even though the opposite is true. And that's what's really happening in Europe : power is shifting more and more locally. Barcelona's increased independence is big. The real power base of the Belgian and Dutch governments is specific cities (Antwerp and the Hague). Outside of those cities, things are going very wrong and support for the government is nonexistent.
Edit: She was, however, probably the best candidate the party had. Ironically, the Labour Party has at least five people in parliament right now who'd make a better Prime Minister, but a fair few of those aren't even in the shadow cabinet.