None whatsoever. Henry VIII separated the Church of England from Rome, i.e the authority of the Pope, but it remained catholic and , as you say, Henry cheerfully persecuted protestants until his death, although he did allow certain reforms, such as the translation of the Bible into English. On the accession of the boy king Edward VI the reformation proceeded apace, leading to a protestant church in England. The heresy laws were abolished, only to be revived on the succession of his sister, Mary Tudor, a firm papist. These were again abolished on the accession of Elizabeth I, who wished for religious tolerance. Unfortunately her hopes were dashed in 1570 by the publication of the Papal Bull:"Regnans in coelis..." in which Elizabeth was denounced as a heretic and a bastard, and it was therefore lawful for any catholic to kill her, without fear of sin. The subsequent persecution of papists derives directly from that bull, as it made all catholics potential traitors. No person ever suffered death under Elizabeth merely for being catholic; those who were executed were either guilty of plotting to overthrow the Queen or were catholic priests who, by their calling and under the Papal bull described above, were by definition traitors.