Well Brexit only had to be dealt with in the first place because the Tory party were haemorrhaging votes to UKIP. Leaving the EU was in no way a majority opinion before the Tory Party decided to appeal to its throbber wing (which at the time was very much a minority) who were threatening to join UKIP (one of them actually did).
Be under no allusions (copyright SWP) the only reason Brexit was even a thing was an act of Tory self-preservation. Remember, even in 2010, after 3 terms of Labour and a global financial meltdown, the Tories actually need a coalition to get into power. It was their solution to offer a referendum.
Its all down to the Tories, no one else