The EU referendum is a proxy for a vote on immigration. If limits could be placed on the right to live anywhere in Europe, people would be completely fine with the EU and would likely be swayed by arguments like the need for unity in the face of neighbouring dictators, free trade, energy policy, climate etc. There are other issues with the EU, around sovereignty, democratic deficit, two-speed Europe, etc, but I don't think the average person really cares about those, they're too abstract.
In principle I think if it could be shown that the current rate of overall population growth (about 450K per year, the bulk of which is net immigration) is sustainable, that might have been enough, but in practice people perceive social systems to be overwhelmed and in crisis, or at the very least that government forecasting and planning is woefully inept.
I suspect if there is a referendum, people will vote to stay in, mainly because no one will paint a realistic picture of what it would mean to leave (the fact that the leaked document was intended to remain secret whereas the governor of the Bank has not been secretive about the case for staying in Europe, is a case in point), so all that will be heard is horror stories about how the UK will become Zimbabwe if it leaves.
Nevertheless I predict it will be a closeish vote, rather like the Scots referendum, 55%-45% or so on a highish turnout.