I know the monarch, the Queen, is the Supreme Governor of the Church, but how did these two bishoprics become the most important and not London?
The Archbishop of Canterbury became the first leader of Christianity in England, because Canterbury was the capital of Æthelberht of Kent when Augustine's mission arrived from Rome in 597. Although it's a very important trade port, London doesn't really approach anything like capital city status until the ninth century, and doesn't really become the de facto capital until the eleventh. Even in a united England, Anglo-Saxon kingship is largely itinerant and based around regional capitals - Winchester, Tamworth etc.
York was the capital of Northumbria, and an archbishopric was established there during the parlous days of the early Church in England, when the establishment of political power from Kent as far north as the Humber seemed highly unlikely within any reasonable timeframe.
Who was the first king to officially make London the capital?