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This is the reason for Cameron's famous speech where he wanted the Tories 'to stop banging on about Europe'. He/his financial backers/ his political strategists had noticed that blue-on-blue EU whingeing always cost the Tories in the polls. Of course he was never in a position to isolate the remnants, and their newer recruits, of John Major's b4st4rds, and ended up, after GE2015, being bounced into a refrendum.
https://www.theguardian.com/politics/2018/nov/17/labour-gains-lead-over-tories-opinion-poll