I don't know if they were persecuted under Queen Elizabeth I. I do know that they separated from the Anglican Church, because they didn't think it was reforming fast enough.
My third son is named after two such English martyrs: John Fisher and Edmund Campion (we named him John Campion.) Fisher was the only English bishop to remain loyal to the Faith under Henry VIII. Campion was imprisoned, tortured, drawn and quartered under the regime of "Bloody Bess" (Elizabeth I) for the crime of being a Catholic priest. Since the time of Elizabeth, the English have been among the chief persecutors of the Faith.