Measurement of income inequality is like measurement of any natural or social phenomenon. We measure inequality as we measure temperature or height of people. The English (or welfarist) school believes that the measure of income inequality is only a proxy for a measure of a more fundamental phenomenon: inequality in welfare. The ultimate variable, according to them, that we want to estimate is welfare (or even happiness) and how it is distributed. Income provides only an empirically feasible short-cut to it.
I would have been sympathetic to that approach if I knew how individual utility can be measured.
Read the article of Branko Milanovic