Chris

Charlie is the ‘titular’ head of the Church of England. He is officially the Supreme Governor, but that’s largely a formal position without executive authority. He does have the right to appoint a new ABC under a 16th century act of parliament but in practice that’s just another one of his powers exercised for him by the government and the government in turn has an appointments commission - although in practice that commission is operated by senior clerics from the church.

The commission votes on a nominee and provided that individual has two-thirds of the commission on board the individual is recommended to the PM. Interestingly, had Rishi been the PM, despite being a Hindu he seemingly would have been able to then approach the candidate and ask them if they want the job, whereas had he been a Catholic or a Jew he would not.