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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.
Velocio-
Indeed. It's been a failure of national government. Thatcher ripped the guts out of a lot of communities by closing the mines and other heavy industries, and no subsequent government has ever adequately sought to regenerate these areas.
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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.
andyp
Oliver Schick
If you allow free movement of people between countries that have vastly different standards of pay and welfare then the people of the poorer countries will migrate to the richer countries and depress the salaries in that country until such time as there is parity across Europe.
This will be suffered hardest by the low-skilled, low-paid of the richer countries - our working class.
The ultimate effect is a rise in inequality as a result of EU migration which is unable to do anything to fix it because it's a technocracy and is resolutely committed to the 4 freedoms, one of which is hugely detremental.