Perhaps the upper house could be modelled on the US Senate, where each County would ellect two "Lords", The US Constitution prescribes that the Senate be composed of two senators from each State (therefore, the Senate currently has 100 Members) and that a senator must be at least thirty years of age, have been a citizen of the United States for nine years, and, when elected, be a resident of the State from which he or she is chosen. A senator's term of office is six years and approximately one-third of the total membership of the Senate is elected every two years.
The UK has 48 English, 32 Scottish and 22 Welsh Counties, so 102, giving an upper house of 204, which would seem to be sufficient.
Sounds about the right number, but if you didn't balance the representation with population you'd rightly have an outcry against England being under represented :-)
We nearly had proportional representation in the lower house, but lost it to the 1st World War, after which the Liberal party wasn't strong enough to see it through.
The 1918 Representation of the people Act offered 190 seats by proportional representation, which proposal wasn't adopted.
https://api.parliament.uk/historic-...esentation-1#S5CV0106P0_19180513_HOC_267The Act did extend suffrage though, so belatedly a good thing:
https://en.wikipedia.org/wiki/Representation_of_the_People_Act_1918