Not quite. There were quite a few “recusants” ie Catholics who refused to turn Anglican. Large swathes of rural areas were Catholic, but even a few city folk in London.
The Earls of Arundell for example are a family of nobility that has remained Catholic for centuries
I have thought for a long time that Shakespeare was one of the secret people who translated the King James Bible. Since the Pope at the time only wanted the Bible in Latin, Shakespeare would not have been Catholic.
The colony of Maryland (named after King Charles I’s wife Henrietta Maria, who was a Catholic) was started to be a refuge for English Catholics (but they were always in a minority there, and the Puritans later abolished the religious toleration they had set up). Charles Carroll of Carrollton, the last survivor of the Signers of the Declaration of Independence, was from one of the wealthy Catholic families in Maryland, but he could not vote until 1776 when Maryland threw off its allegiance to the British crown.