The gap just gets wider and wider

Abolish the House of Lords and replace it with elected experts in various fields who are paid a wage.
Boris Johnson could probably do that with a majority like his.

I don't know how the elections would work, though. I couldn't sensibly choose an expert in genetics, for instance (or lots of other things besides) as my expertise wouldn't run to that.

Ultimately, it would come down to charisma, or PR, or how well the experts could influence the media, and as only a few genuine experts have that - often a career in a lab or a library mitigates against it, or maybe those who are ore introverted are drawn to that sort of life. Either way, I can't see an elected HOL working in practice.