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.