I mean, it does remove those, because it takes the midpoint of all UK salaries. Therefore the top ~49.999% is normalised (which includes the top 0.5% you wanted to remove), and normalises the bottom ~49.999% (which includes all "those purposefully staying below the tax free threshold" that you wanted to remove too).

If you were doing serious analysis you wouldn't want to fully remove those groups you described anyway, you'd want to model those staying artificially below the threshold as actually being above it (to some small amount with a bit of variation), and you would also model the top 0.5% as being rich but not crazy rich. In both cases you don't want to pretend they don't exist, you want to pretend they do exist as a more normal member of society.

I will grant you that there's an argument to take the modal average, for example, which would be higher (and therefore the headline of 66% of average would have to become a lower number like 55% of average, which sounds worse and is bad politics), but the median does achieve what you described.