Brexit wasn't direct democracy; the public vote was a non-binding referendum submitted as an electoral strategum by the elected government, which then quit in favor of a new government of the same psrty, which decided—though in no way legally compelled to—to treat the vote as if it were a binding order in order to pass responsibility off onto someone other than itself.
In an actual direct democracy, the people would vote on the actual policy details, not vague generalizations only if and when it seemed likely to serve the political strategy of the ruling officials.