Millicent Bagnold was Minister of Magic before Cornelius Fudge, from 1980-1990 (OP5). She was a “highly able Minister. Had to answer to the International Confederation of Wizards for a number of breaches of International Statute of Secrecy on the day and night following Harry Potter’s survival of Lord Voldemort’s attack. Acquitted herself magnificently with the now infamous words: ‘I assert our inalienable right to party’, which drew cheers from all present.” (Pm)
The Muggle Prime Minister at the time of Bagnold's tenure was Margaret Thatcher. There must have been some interesting meetings between the two women!