“How I can annul someone's status as a godparent of my child?"

The following is taken from Legal Opinions Concerning the Church of England and appears to have been part of the 1994 text of that document:

Godparents : Removal and Replacement

There is no procedure to enable the parents of a child to remove a person as godparent of their child and substitute another person in his or her stead. Godparents have no obligations in substantive law and there is no legal significance in a particular person being godparent. There is no reason why parents should not make an informal arrangement with other persons to act as additional “godparents”.