Edit: The study linked above [0] showed the following for voter regret (specifically "do you have doubts about the way you voted?"):
Remain
Yes / No / Don't Know
98% / 1% / 1%
Leave
Yes / No / Don't Know
90% / 6% / 4%
[0]: http://www.britishelectionstudy.com/bes-resources/brexit-bri...