Actually that was by design of the anti-Brexit faction.
Before you get ranty at me - I voted remain. But your comment is revisionist. The pro-Brexit shysters were not in power. After the referendum, whichever way it went, the pro-Brexit people were not going to be given power, it was not an election.
They had no mandate to implement anything. Any plan they promised would have been irrelevant to the UK government and had no more force than you or I scribbling on a pub napkin.
You know who was in power, who was in a position to make a plan, arguably whose duty it was to make a contingency plan if the referendum went south?
The very pro-EU faction at the head of the Tory government. But they didn’t. They told the public they weren’t making a plan so that it didn’t look like a low-risk option that the country could go for and be OK. The lack of plan was no accident, it was a Remain-side tactic.
The Brexiteers were/are wrong, hateful, shysters in so many ways. But your ire in this specific case should be aimed squarely at David Cameron. The Brexit shysters just didn’t have any power, and Brexit voters voted without a plan because it was the choice they were given.