Yes

Yes technically the Church of England is more an endowed church than an established one, and this is how the matter stands in comparative law - much like the old situation of the catholics in the Irish constitution at the old article 44 - they are simply recognised as the majority faith but only because they are a standard majority - and that can change too as numbers of catholics increase so rapidly, and thuswise the CoE retains some independence from the sphere of the temporal in civil law. It was always said that CoE canon law became UK domestic law by dint of the Commons and parliament assent and the Queen's own assent, but this is illusion and grandiose pretension, more civil effects than a real blessing of the civil temporal force. Besides the two sees of York and Canterbury remain the spiritual directors of the prime minister. And these alone.