I think the aim of Brexit was to remove power from Brussels, the subject of the balance of power between parliament, the executive and the people wasn't really on the ballot paper.with representative democracy, there's an issue with referenda, which is why we rarely have them. A referendum chooses Course A, but what if Parliament wants Course B. And parliament is made up of people chosen by people...all the more difficult in this specific case when one of the aims of Brexit was to 'give back power to Parliament'.
Parliament chose to have a referendum. It's a particularly duplicitous and/or arrogant politician who says yes we'll have a vote but if it doesn't go the way we want we'll ignore it, or notionally follow it but fiddle the outcome so that the result is not actually what people voted for. It's also in my opinion a particularly stupid one because I'm pretty sure the electorate will remember. That's why Ken Clark can afford to get on his morale high horse a) he's not seeking re-election b) his constituency voted remain. That as a high profile Tory he will damage other candidates chances by making the Tories look like a party who don't stick to their promises presumably is beneath his self interest.