Electoral Disfunction

I know it may seem an odd and obvious thing to break a year's worth of radio silence over, but how come the British Conservative Party MPs (and to be fair, the Labour Labour Party, when they have their leadership shenanigans) get to use a different and better way electoral process than the British people use for choosing MPs? 

Instead of a 'winner' takes all system, where whoever get the most votes in a single ballot, no matter how miniscule that total is, they get to use a series of run offs, with a dwindling pool of candidates - effectively Alternative Vote.

(To answer the question posed in the opening paragraph - the British electorate had a referendum on Alternative Vote a few years back and rejected it because they were uncomfortable with counting to five.  Which begs the question(s) - first, have they changed their mind now 63% of MPs represent Labour, based on a feeble 33% of the vote - the most unrepresentative result in British electoral history?  And second, if the answer to the preceding is "No" - can we take that as an admission they think their MPs are just lots cleverer than the British people? )

Had MPs been required to use the same antiquated, nonsensical First Past The Post as the rest of us, Robert Jenrick would have elected leader quite some time ago, based on a whopping 23.7% of the vote; or if they had continued the idiosyncratic "Members get to choose from the final two" concept, the options would have been Jenrick or Badenoch - a very grim choice for anyone who isn't outright bonkers.