Well, there's still the little matter of the 17 million who voted leave...
Does not matter much in the big picture. The very public, powerful and 'passionate' leaders of the leave campaign are falling like dominos. Parliament has no requirement to even acknowledge the leave win, at best it serves as an advisory note from the general public.
Yes that might be classed as not catering to a democracy, but the general public won't care, or not care enough to riot over this. Plus their political voices are being silenced day after day with all the leave bigwigs jumping off like rats on a sinking ship, which fuels people who voted leave to change their tune, the collapsing of the political power and voice of the leave leaders is not a good look at all for the leave voters.
The next PM, if they voted to remain, and it looks like the candidates who did (esp may) will win, will delay triggering article 50 until the next gen election in 2020. It will most likely be difficult as hell extending the timetable to leave the EU, however expect heavy, private negotiations to try and get more time.
Then, introduce a second referendum in 2020 via a general election, the public, even the staunch leave voters, would have long forgotten about the first referendum outcome by then, and due to the second EU vote and then general election, feel as if their voices matter once more.
Of course all of the above is at this point, merely predictions. Could be a leave supporter become the next PM and pulls article 50.