Re: From another angle...
It was an advisory referendum - of itself it confers no power nor to do anything.
We put military involvements in other countries to the vote, or at least debate, in parliament before sending the (more?) aircraft in. Why wouldn't you do same with something that represents a major shift in geopolitical alignment?
The PM that pushes the Article 50 button and doesn't come out of the negotiations with a good position will find themselves marked down by history. And anyone who aims to be PM and says that they don't want to be fondly mentioned in the history books is either lying or so egotistically cocksure of their divine right as to be dangerous.