Pardon my pedantry, but ...
It was under Matthew Parker, not Thomas Cranmer. The issue was not the Thirty-Nine Articles (which have problems galore, but still weren't the issue), the issue was Rome's view that the ordination rite enacted in the 1662 (I think ...) BCP was invalid.
Some Anglo-Catholic clerics have tended to concede that Rome had a point and had themselves conditionally re-ordained by Old Catholic bishops (who had valid orders until they started ordaining women to the episcopacy).
Thanks for the information.