Henry II struggled with the Roman Church over whether the clergy were subject to civil courts for civil crimes.
The first clause of the Magna Carta affirms the freedom and independance of the Church of England. This was a repudiation of King John’s submission to Pope Innocent III.
Henry III surrounded himself with Italian advisors who looted English estates for the benefit of Rome. The barons and commons revolted and forced Henry III to get rid of them in order to keep his throne.
Edward I abolished the practice of bishops in foreign lands owning English estates for the benefit of their foreign aristocratic patrons. He also established a legal code that accomplished much of what Henry II fought for in terms of the clergy. One could reasonably claim that Edward I did nearly as much to curb the power of foreign bishops in England than Henry VIII.
The Hundred Years War pitted the English against the French, who held the Pope in Avignon.
The Northern Rebellion was one of several attempts to overthrow Elizabeth I. The perpetrators of it and of other conspiracies (some of which were Protestant) were rounded up and executed for treason. Given the half-hearted “Pilgrimage of Grace” snuffed out by Henry VIII, it is safe to say that the English people were not terribly attached to the Pope.
I would say that's a generally overbroad statement.
From what I understand, Eamon Duffy has done research on the faith of the English people prior to the English Reformation and wrote a book about it titled The Stripping of the Altars. Sadly, I can't say that I've read it.