I've long been of the view that inequality is overstated in the UK. For the very simple reason that we measure it by incomes and not by consumption. But of course, if you really are worried about inequality it must be inequality of consumption that you are worried about. And I've also long thought that UK inequality is likely to be much more overstated than the inequality of most other European countries. For our economy is dominated by London in a manner that no other European country is dominated by just the one city. The mechanism here is of course that London property prices are hugely higher than they are elsewhere in the country. And so are London salaries: but that second gets recorded as inequality of income when that first means that that is pretty much evened out by the equality of consumption of housing possible for that greater sum.
Sadly I've not seen any research that details this for the UK. But here's a nice paper that worries away at the same problem for China. Yes, China is unequal, more so than the UK or US. But they look at the variability of housing prices across the country and then take that into account when comparing the variability of incomes. And quite a bit changes:
The overstated inequality if using nominal income data is not as great if inequality is measured with the Gini index (in Figure 2, both the Theil and the Gini have been scaled to equal 1 for real inequality at provincial level). Nevertheless, not deflating for spatial cost of living differences still causes an upward bias in the Gini coefficient of 15-16%. Taking an average of the results for the two inequality measures, in round figures approximately one-quarter of apparent spatial inequality in China disappears once account is taken of cost of living differences, where these are just coming from house prices.
If, as they surmise could be true, the differences in housing prices represent a general change in non-tradeable goods prices then the reduction in the Gini measure of inequality would be greater.
Which brings me back to the UK. We do have high inequality in the UK as compared with other European countries. But I'm convinced that some of this is the effect of the much higher incomes available in London. And those higher incomes are rather offset by the higher costs of living in London: meaning that consumption inequality is a great deal lower than everyone thinks it is.