I believe the Church of England has time and time again, shown itself to be completely out of touch with the opinions of the man in the street, and modern Britain. The people in charge of the church have not been elected by the public, and have no place having direct involvement in the running of the British state.
I definitely think that the Church of England should separate from the British state. I think that one should not be affiliated with the other. Nor do I think that there should be public funding from tax payers for any type of organization based on religion. That is why I think that the British state should be independent of it.
I believe that Church and State should always be separate entities, the time that the church had considerable political and military power in the world is long gone and the church shouldn't be connected to the state in any form, I feel that it would be the correct thing to do.
It would not be catastrophic if the church of England were to separate itself. They would have less influence over the government, but that would remove scrutiny of the church being too politicized. Likewise, opponents of the church would not automatically dislike the British state as well. The two each have their own critics, and neither is gaining too much to lose from the partnership anyhow.
No, I do not think that the church of england should try to take itself away from the british state at all. I think that this will have a lot of bad affects on the church, and that it will end up making a lot of problems for them later.