Even so, it was still well within the margin of error. Your rounding was misleading: the referendum result was 51.9% to 48.1%, almost a 4% gap.
It also still assumed, probably incorrectly, no remorse on the Remain side to cancel out the remorse from Leavers.
But probably more significantly than any of that, I think every other poll I've seen from reasonably credible sources in recent months has pointed the other way. The one you're talking about appears to have been an anomaly.
https://www.politicshome.com/news/europe/eu-policy-agenda/br...
Regarding detailed analysis, you might find the Ashcroft polls interesting if you haven't seen them before. He did a write-up shortly after the referendum[1], primarily about who voted which way and why. Then there have been a couple more interesting ones just a few days before today's announcement as well[2,3], looking at current expectations regarding Brexit and more general voting intentions.
Spoilers for [1]: The top three reasons identified for Leave voters were (most significant first) sovereignty, immigration, and lack of control over ever closer union and EU expansion in the future. The top three reasons identified for Remain voters were the economic risks of leaving, Single Market access without being in the Eurozone or Schengen area being seen as the best of both worlds, and the feeling of becoming more isolated if we left.
Spoilers for [2]/[3]: Everything you've been assuming about the Tories being dominant in British politics today is true, except that you've probably underestimated just how utterly dominant they actually are and how unpopular both Labour and the Lib Dems are. It's going to be a long few weeks if you're not a blues fan.
[1] http://lordashcroftpolls.com/2016/06/how-the-united-kingdom-...
[2] http://lordashcroftpolls.com/2017/04/new-political-landscape...
[3] http://lordashcroftpolls.com/2017/04/more-from-my-brexit-res...
So 4% of 'leave' voters regret voting leave and 2% of 'remain' voters regret voting 'remain'. So in total it's about a 2% shift which would reverse the current result percentages.
No, it wouldn't. Your maths is off by about a factor of two, one way or another.
http://www.independent.co.uk/news/uk/home-news/brexit-leave-...
"Four per cent of Leave voters polled said they thought Brexit was the worst thing to have happened this year,"
The result was 51% leave 49% remain, it would be the reverse if they could vote again today.