EU referendum, brexit and the aftermath

Compulsory voting plus "none of the above" option.

STV for wholly elected House of Lords, since the lords is exactly where you'd want the least objectionable/extreme candidates to end up.

Elect commons using some form of PR:

1. No more safe or swing seats, no more wasted votes, no more tactically voting Con/Lab/LD to keep the Con/Lab/LD/UKIP candidate out when you really want to vote Green/SWP/MRLP/Other.
   
2. Allows large parties which currently try to satisfy multiple significant factions to have distinct identities at election without actually losing power.
   Far-right-[Daily Heil]-Tories could split from Centre-right-[The Times]-Tories without joining UKIP. "The Labour Right" could break away and stop pretending to be left wing.
   
3. With PR and smaller parties, Cameron wouldn't have put EU Ref in his manifesto to stem the flow to UKIP whilst probably planning to abandon it in the coalition negotiations that never happened because he was too successful and Clegg failed to distance LD from the more toxic Tory policies enacted by the Con/LD coalition.
   
4. Not having big "~30% of the vote" parties would reduce the power of the media. It might only take once well-spun story to sink your preferred party's main competition; burying 4 different "10%" parties who seem likely to form a coalition is a lot harder.