The vote was not binding, parliament could vote against the result but it would be doubtful that they would. It is down to things being done by the letter of the law and parliament having it's say on how negotiations are carried out.
As for how you discribe the liberal media, that echoes more our rightwing media which supports our Conservative party (They are more like the Republican party over in America.) Labour are our other main party and are a socialist party tied to the workers and unions. We do have Liberal Democrates, the Scotish National Party and others who also have representatives in parliament. It's far more varied than the 2 party system that dominates in America.