If a political party leader officially calls for a referendum and submits it for the vote in the parliament this question will resolve to YES. (Currently Green Party advocates it but there is no concrete step.)
Edit and clarification: all that matters is if a vote is held for a referendum. Who initiates it and how, and even the result itself does not matter. If an actual decision is made to hold a referendum somehow in another way(very unlikely imho) it will still count.
Edit & clarification: I am personally participating in this market as the result should not be subjective.
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Can you be more specific? There are lots of tiny political parties in the U.K., so there’s probably already one that supports joining the EU. But you talk about a vote in Parliament, so is the condition that the party has at least one MP? And does the leader have to personally start the vote in Parliament (some parties have representation in Westminster but don’t have an MP as their leader, eg the SNP)?
@lisamarsh I mean like I added to original description, support by itself does not mean anything. As is Green Party already supports it, but they say “when the time will be right”. Hence it doesn't count. What counts and matters is an actual vote in the parliament regarding a referendum. How and who initiates a vote is not that important. I just assumed a vote will most probably start with a specific party leader openly supporting it.
@FatihKurt What if, say, a random Labour MP causes a vote in Parliament on the issue (eg through a private member’s bill) without rejoining being the party’s official stance?
@lisamarsh You re right about that case. I clarified in the description that, all that matters is if a vote will be held.