The Church of Rome. It is an island because it is isolated or cut off from the world. It is a ringing island because bells are incessantly ringing: at matin and vespers, at mass and at sermon-time, at noon, vigils, eves, and so on. It is entered only after four days' fasting, without which none in the Romish Church enter holy orders.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894