If you click the button that removes the don't knows (effectively apportioning their votes in the same proportion of remain/leave percentages), the gap is very close (no more than 12%* in one poll) but generally a consistent 4-8% gap. I wouldn't count that as a significant lead. One thing is certain, those with a desire to remain are much more likely to engage/register their feelings so it is unclear if that gap should be a little closer because a lot of those with a desire to leave are not engaging. In my opinion, there's definitely an edge for Remain, of course, but running a referendum could easily return a 52/48 split reversal and what happens then?
Meant to add in that it is best to ignore some of the very wide spike differences as outliers as these generally suggest a response to something specific in the news or a dodgy poll.