Why particularly the CofE?
There's lots of other institutions that aren't as big or as visible that have issues that they can keep hidden because they don't hit the headlines in the way the CofE does.
What about the Scouts, for example? Or local theatre groups? After school clubs? etc.
I think that the denominations should have one independent group between them that anyone can go to with concerns, because some of the smaller denominations can smugly know that they probably won't hit the headlines because the general public hasn't heard of them but they're so small that any investigating body if they don't know the person they are investigating well, they know several people who do. Which means it's easy to sweep under the carpet, and the victim has nowhere to go.