Just one example - Sarum Chant, which unlike Gregorian is metrical (typically triple time) and characterised by what a musical historian of the time called the "contenance Anglais." Here is a very late example by the great Thomas Tallis - who remained Catholic despite persecution, and along with his fellow-Catholic, student, and successor William Byrd ("our Fenix") was protected by Queen Elizabeth for the sake of their glorious music. Here, Renaissance polyphony is interspersed with the Sarum Chant:
Audivi Vocem de Caelo ("I heard a voice from Heaven")
Henry did not wish to change anything other than placing himself as head of the Church in England, and looting the substantial assets of the monasteries to fund his inflationary policies and reward his friends. It was his son Edward, a child ruled by radical Protestant advisors, who oversaw the destruction of the Church and all its treasures: liturgical, musical, artistic.
The unintended consequence that really hurt was that the Church had been funding all the hospitals, orphans' homes, pilgrims' refuges, and poor relief. Only after the English belatedly realized that they had cut loose all the suffering in the realm to fend for themselves, did stopgaps like the Poor Laws and workhouses come into being. They didn't work nearly as well.
Thank you for your post.