It is suggested that any by-election result be fed into the voting system by:
The system would then automatically recalculate the voting "power" of every MP in the UK country in which the by-election took place, in order to reflect the new voting proportions.
In practice, the difference would be small over the country as a whole, but it would still move the balance of power in the direction indicated by the electorate in the relevant constituency, demonstrating the electorate's satisfaction or otherwise with the ruling party's (or parties') performance.
Following the 2010 UK General Election, a by-election occurred in the Leicester South constituency in May 2011, and the relevant re-calculation shows the resulting small differences in English MPs' voting powers.
[To follow shortly]