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I agree that the EU is not a socialist paradise. And it varies a lot per area, Portugal for example despite poverty still seems to have decent healthcare. Right wing by itself can mean several things. It's neolib that's very damaging.
But if the EU is, on average, less right wing than the UK it will still have a tampering effect.
I'm not sure what socialist paradise the UK can join with. Canada has a nasty deal cooking that is in parts as bad as TTIP despite the current left wing government...
Reality.
This was the situation in late 2015. Red is leftwing.
And Hollande was on 13% approvability last time I looked, so France is likely to head right. Greece is left, but has to implement right wing policies under the auspices of the EU. And the right wing in Sweden is gaining a lot. Hardly a socialist paradise.
edit: source of map - http://www.newstatesman.com/culture/observations/2015/10/why-are-right-wing-parties-thriving-across-europe