Simon Kuznets predicted that as an economy develops inequality will rise and then, at a certain stage of development naturally begin to fall back again.
It would seem that he was reasonably correct as well. These estimations of historical income inequality indicate that the Gini was around 51, 52 for the UK in 1801. Current day income inequality in the UK is again around 51, 52 as measured by that same Gini. Those for Sweden and the US are similarly around 48 at present. Now, of course, it is possible to change that inequality of market income through the tax and benefits system and every country does so by various means, lowering the outcome inequality. Some more than others as we know.
However, if that rise in inequality is indeed part of the development process it means that worrying about rises in inequality in China, or India, at their current stages of development is a little silly. We'd do better to not worry about such things (as all too many "in development" do) and concern ourselves with the growth which itself will lower the inequality.
There's another point to be made here as well: which is that the current measures of inequality, by income, grossly overcount the amount of inequality that we do have. Way back when a Gini of 52 meant that some would eat well and others would starve. Now it means that some shop at Fortnums and others at Spar. The difference between having cheaper food than the rich and having no food unlike the rich is a measure of vastly lesser inequality in the modern day. It wasn't until the 1970s that the majority of British households had a fridge: the difference between having one of Comet's best and £8,000 worth of Smeg is hugely smaller than that between a larder or an icebox and a fridge.
We both overmeasure the inequality in our own society and worry overmuch about it in others. Time perhaps that we stopped doing so.