Trouble with Referendums: who is accountable for its delivery?

Nick Cohen makes a point I shared privately with several Leave friends during the EU Referendum campaign last year:

Vote Leave dissolved as soon as the contest was won. The referendum thus dispensed with the most basic democratic requirements. The winners were not accountable for the promises they made. In their history of the campaign, Jason Farrell and Paul Goldsmith quote the Leave campaigner Gisela Stuart saying that she thought the referendum was an ‘abuse of democracy’ because no one who campaigned to leave was accountable for what happened next.
It seems a little rich of Ms Stuart to wring her hands now the rest of us must live with the consequences of the Brexit she fought for. But her point remains a good one. The leave campaign could make the most fantastic promises and tell straight-out lies because it need never live with the consequences.

He continues:

In these circumstances, Brexit can mean whatever you want it to mean. Because the referendum boiled down all the complexities to a deceptively simple question, because the men and women who brought us leave are not answerable for their actions, the scope for demagogic politicians to claim the people have been betrayed is vast.
More than a year on after the referendum, with the Article 50 clock ticking, we still do not know what British policy is.

The really queer aspect is how it compels political representatives to act against their own better judgement, on the advice of what was and remains an opinion poll.

Power without responsibilities. Hmmmmm.