Christianity in England was not the cause of the Crusades so I'm afraid you're new point is still wrong. Crusades were the pope's idea (he lived in Rome if you're wondering - that's in Italy - and was French by birth). In fact most crusaders and leaders were French although other countries certainly contributed.
So no, the Church of England was not responsible for the crusades. Nor was Christianity in England (still different things I'm afraid). You might find this information about the crusades useful to start some research.