It is hard to point to any one event that caused the balance to shift to "LEAVE".
But it is simple to point to one which, had it not happened, might have prevented the shift.
That event was the needless waste of the use of Air Force One for America's Kenyan President to jet into The UK and personally deliver a threat of dire consequences should Britain not play it His way. The Brits do not respond well to threats.
Had He stayed at home and just contented Himself with another round of golf the world might be a different place today. True, a slightly less free place, but is that not what He would have wanted had He but a glimpse of understanding about the consequences of His Imperial delusions?