I think it's fair to say, though I haven't done exhaustive research, that the proportion of Church of England clergy supporting the European Union is greater than that of laity or non worshippers. And Archbishop Justin Welby has confirmed that he is firmly "in".
We need to think hard, to avoid knee jerk reactions. It's easy to caricature a bureaucratic organisation that, although allowing some nominal democracy, has unelected officials to decide things for us.
But the Church of England has its good side as well.