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when the inequality in every other country in the UK decreased
I assume you meant 'EU' here. There are a lot of studies that suggest inequality in Europe has increased in recent decades, however. Here's one as an example:
Specifically on Germany:
https://www.theguardian.com/world/2014/oct/23/wealth-gap-inequality-germany-higher-study
I believe this is because the European ideal was quite thoroughly betrayed by certain governments in the 1980s and 1990s. I personally think there is still a lot that is great about the EU, but there is a problem with increasing the size of markets, as it tends to create oligopolies shared between only a few large companies, or at the least tends to favour larger enterprises over small and localised ones. Needless to say, this can all be addressed by maintaining proper tax régimes etc., but that hasn't been done. Remain and reform.
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Ah, maybe my statement would be better qualified as "UK inequality was greater before the EU, and remains greater than other European countries in the EU, whilst increasing at a faster rate than other countries in the EU".
It remains true that the UK's problems are of the UK's making, not of the EU's making.
Social and economic inequality has been measurably greater in the UK before we joined the EU, and in-spite of having joined the EU (when the inequality in every other country in the EU decreased and social mobility increased - in the UK the opposite happened).
What inequality exist in the UK is 100% attributable to the UK, not the EU.