"The legislation is irrelevant. "

And with the one statement you prove how TOTALLY out of your depth you really are.

The legislation is everything. Britain isn't  a third world banana republic where people just change laws on a whim. Anyone living in Britain has full recourse to the legal system - it's what the Brexiters demanded  - British Democracy! 

No one is stopping the result being carried out. It is HOW it is to carried out that is being questioned - Ask 2 Brexit supporters what they voted for and you will get at least  3 different answers. 

And yes, there is a real risk Parliament decides to ignore the will of the people, they might even dissolve Parliament and run an election - which would be VERY British.