The Labour vote was a popular vote, it just happened to include union members and 'registered supporters' who weren't party members (but would have had the same outcome in 2015 without them). The electoral college system was abandoned by Miliband, and Starmer has given up trying to bring it back in some form.

The Tories haven't got to worry about having self-styled radical socialists on the ballot but have had exactly the same problems: candidates that appeal most to the Tory selectorate like Iain Duncan Smith and Liz Truss are neither in touch with the public mood nor competent.

Not sure that a presidential system with a public vote would necessarily do better though. The public loved Johnson and liked May at first.