Brexit has put the UK in an impossible position. This Venn diagram explains why
From what I understand (I am not a British citizen) the plan seems to be to delay triggering Article 50 for as long as possible, and then get the actual triggering to be voted in Parliament (expecting Parliament to vote against it and therefore nullifying the Brexit).
This will dilute the (understandable) feeling of betraying for Referendum voters, especially if during the intervening period media and UE will scare people in believing that an actual Brexit would be a catastrophe.