David Cameron thinks FPTP is a wonderful voting system and should continue to be used for parliamentary elections.
This being so, how come the Tories don’t use FPTP to elect their leader? (If they had, David Davis would have won). Instead, they use a multiple round runoff system, where the candidate with the least votes in each round is eliminated and voting proceeds again (as a twist: the electorate is Tory MPs for all rounds, except the last, where the entire Tory membership gets to vote).
Labour also use a runoff system instead of FPTP, but instead of having multiple rounds, they compress the voting into one round using AV.
The reason the Labservative parties do this is they know full well that FPTP is a crap way of choosing someone in accordance with what the voters want. Both parties in their internal elections want a leader who speaks for a majority inside the party, and they know that if they used FPTP they’d be less likely to get such a leader.
The Labservatives support FPTP for Westminster, not because its a good system, but because it’s a bad one, and can be relied upon to prop up the Labservatives’ cosy little duopoly that’s served them so well and Britain so badly.
The Labservatives are parasitic on the British body politic — as an example, consider their MPs’ expenses scam, that went on for decades under Tory and Labour governments — and I doubt this country will be well governed until their stranglehold on power is broken.