I'm very centre politically but I was on the Leave vote from the start, I'm not sure I would have even changed my mind with a strong campaign from remain, but I know plenty of others who may have. I wrote a massive post around the time of the referendum as to the reasons, I've alluded to one of these only a day or two ago.
The EU has good and bad aspects, but I feel the bad outweigh the good. I feel that the EU should be a 2 tier system, with 2 currencies, It should have allowed free trade between us all, but things like currencies and FOM, could only be shared where living standards and wages are similar. So you would have the likes of Germany, UK, France, etc in one zone and then the poorer countries in the other zone, the likes of Greece can't even devalue.