Henry was perhaps the only Catholic without the Pope. In many respects he maintained RC Theology except those areas which necessitated the Pope. Excommunicated though he was, Henry would certainly not have considered himself a Protestant, despised Luther, and was very well read theologically. Henry considered himself in the line of Mediaeval Christianity, certainly not a Protestant.
Here are the X Articles of Faith which Henry promulgated post-Divorce:
Ten Articles of 1536
As you can see they are basically Catholic.
It is Elizabeth really who begins the C of E as we know it.
But you are right that catholic small c is universal as most Churches describe themselves this way.