I think we either have a representative democracy, and leave the MPs to it, or we should have a directly elected executive.It's just wrong that 81k people chose our PM, the position holds such importance and power.
This isn't a new sentiment, I remember Callaghan and Brown facing a furore too, also arrogantly swept aside.
Having this weird halfway house where we elect MPs and then they subcontract the job of picking their leader to a tiny, self selected minority of the population feels like self-destructive nonsense.
I think referendums are bullshit for much the same reason.