Tbh I think the "easiest" single thing which would improve the UK immensely would be to ditch FPTP and bring in some type of PR voting.
Would a general election be called?
It's a bit farcical that the country will have a PM that was not the leader of the governing party at the last election.
Granted with the Brexit mess they could arguably have some legitimate reasons for not calling it straight away but it seems that they've all ruled out calling it at all, AFAIK.
Ireland has a form of PR (single transferable vote), they've had plenty of instances of the Taoiseach (PM) being replaced and not going to a general election straight away.