Be careful what you wish for.
A second referendum would do enormous damage, not least by convincing significant swathes of the country that our democracy was irretrievably broken, thus opening them up emotionally to be receptive to some form of extreme nutterage. It is a well-travelled path to extreme government, though not generally in the UK.
However it goes, one half of the country is not going to be happy with the result and, if we have a second referendum, why not a third or a fourth? Why would any subsequent referendum have more authority? Why should it be respected more than the 2016 result? Where does it all stop and on what basis?
Finally, combine a referendum and a GE and you'll have a government defined by the subject of the referendum with all the other issues pushed to the back. I doubt we would get much joy from the outcome and it would define the mixture of the next Parliament - so we'd be living with a Westminster defined by Brexit/Remain for the next five years when the need is for unity and to move on after March.
As I wrote in an earlier post, it's up to everyone involved to understand that there are profound, possibly even existential, issues now in play with serious implications for civic peace. Even the British constitution, with all its famed flexibility and robustness, cannot put up indefinitely with the degree of anger, intolerance, ignorance and vehemence that is now such a feature of British political life. People need to understand that they're playing with fire because the referendum is deeply visceral and has now become more than simply a question of whether we leave or remain.