Recent polling has put the Remain camp slightly ahead of the Leave camp, after having struggled in late February when voters didn't appear to respond well to Prime Minister David Cameron's EU demands.
Recent polling by YouGov now puts Remain on 40 per cent of the vote, compared to 37 per cent who want to leave.
Yet, in reality, Remain is likely to be in a much better position than these polls suggest, with current opinion polls not necessarily a good guide to how people will end up voting.
For context, YouGov has found that people often decide how to vote in referendums much later than in general elections, with polling far more volatile than in general elections too.
Think about party voting: many people will consistently vote for the same party across elections, so they always have a good idea of how they will vote in the general election.
But take some recent referendums, instead.
In 2011, the public went to vote in the Alternative Vote referendum. Early polls indicated a large lead for Yes (that is, people wanted the voting system to change from First Past The Post). But in the last months of the campaign voters drifted towards No, and as we all know, the voting system is still the same.
Or take the Scottish independent referendum in 2014. There was a solid lead for the No campaign until polls dramatically narrowed in August 2014, before swinging back towards No in September.
Then consider what professor Matthew Goodwin, fellow at Chatham House, says: "When it comes to referendums we know from research that as polling day nears voters tend to (though not always) become less supportive of the change option."
And the problem is made worse for those who support Brexit, when you consider that last year there were a series of events that should have led them to a commanding lead. Unemployment rose across the Eurozone last year; there's an ongoing refugee crisis, with an horrific terror attack in Paris; record net levels of migration to Britain are persisting. Still, Remain leads.
Yet, current opinion polls on the EU referendum may not be gauging actual public sentiment too accurately, and with campaigning proper just a matter of weeks in, it is all still to play for.