Unnamed Muggle Prime Minister

From Hpwiki

The British Prime Minister of Muggles, unnamed during the course of the story, first learned of magic on the day he took office, when his wizarding counterpart Cornelius Fudge visited him. Since then he has been visited several times, although usually just as a courtesy. On only one ocassion was he asked to act. (To help apprehend Sirius Black.) The arrival of the Minister for Magic is heralded by a talking portrait in the office of the Muggle Prime Minister. (Much like the portrait of Mrs Black at Number Twelve, Grimmauld Place, this picture has proven extremely difficult to remove.)

The timeline commonly accepted in the fandom would make the British Prime Minister at the time of Half-Blood Prince, John Major. (Major was British PM from 1990 to 1997.) However, mention is made of the Prime Minister in HBP having a male predecessor. This is incompatible with John Major. It seems likely that Rowling's PM is a wholly fictional character inspired by multiple British Prime Ministers.