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I don't think it alienates any of their base.

FWIW, I know from immediate personal contacts that it does, and not in entirely trivial numbers. I'm in one of the most pro-Remain areas of the country, but also a LD/Lab marginal, so it will be interesting to see what happens as a result. I suspect it won't make much difference here, but if the same effect is evident in more moderate parts of the country, it could actually hurt them.