No. Hadrian IV. was an Englishman; Martin IV. a Frenchman; Zachary a Greek; Gregory III. a Syrian; Hadrian VI. a Dutchman. The present Pope happens to be an Italian, but the Cardinals could quite easily elect an Englishman next time, should they think fit.
Radio Replies Volume 1 by Rev. Dr. Leslie Rumble MSC and Rev. Charles Mortimer Carty
