Nation where English protestant rulers employed brutal tactics against the local catholic population?
The English Catholic Church is just that, a Catholic Church in union with the pope in Rome. It is no different from any Catholic Church elsewhere in the world except that the language used is English. While the Church of England (Anglican Church) claims to be "Catholic" they are not in union with the pope in Rome so are considered as a Protestant denomination and not Catholic.
There is really no "Roman Catholic Church", although that name, in English, usually refers to the Catholic Church. It came into popular usage in England following the protestant revolt, and has become widespread in its usage especially in protestant and secular English speaking countries. It is rarely used in the Catholic Church and never in official documents.