The church or England claims to be both catholic and reformed
and many of their congregation refer to themselves as anglo-catholics and take offence to being called protestant, is it possible to be both catholic and reformed ?
I was an Anglican for 30 years – trained as a priest.
Anglicans can be somehow “both” Catholic and Protestant – even though that is, of course, impossible.
Anglicans believe they have valid Apostolic Succession. Many “Anglo-Catholics” believe in seven Sacraments, the Marian dogmas, even the primacy of the Bishop of Rome, and concur on Catholic moral positions, including the teaching on divorce. So it is entirely possible for a High Church Anglican in his spirituality and in his doctrinal affirmations to be “more” catholic than two-thirds of the Catholics who go to church every Sunday. When I came into the Church, the RCIA director asked me: “Is the Catholic Church Catholic enough for you?”
That said, there is a broad spectrum of permission in Anglicanism, and there are many (if not most) Anglicans who would not even qualify to be called good Protestants (if by that you mean Christians). The difference between Anglicans and Catholics who hold questionable ideas on faith and morals is that the Catholic Church actually stands for its teachings, while “liberty” is tolerated in Anglicanism.
At bottom, the “test” of catholicity is Communion iwth the Bishop of Rome. That is why so many Anglo-Catholics (like me) wind up on this side of the Tiber. One day you wake up and realize you can’t pass the "duck test: you walk like a Catholic, you talk like a Catholic, you think like a Catholic, you
pray like a Catholic. To be an honest man, you need to become Catholic in name as well as in fact.