The veteran former minister’s personal revelation came after official documents released this week showed how former PM Baroness Thatcher tore into her erstwhile protege’s handling of the economy and government.
The files disclosed how relations between the two quickly soured after Mr Major entered Number 10 following Lady Thatcher’s shock resignation in November 1990, as she accused him of trying to ditch her legacy.
Baroness Trumpington, who was a minister in both the Thatcher and Major governments, disclosed her own knowledge of the bad blood during an interview with BBC Radio 4’s Today programme, which she guest-edited with her son.
Asked if there was a single characteristic needed to be PM, Lady Trumpington said: “No. It’s the luck of the draw.
“Who would have thought John Major would ever become Prime Minister?”
Reminded of the joke that he “rose without trace”, she said: “Absolutely.”
She continued: “He used to ring me up and say that he was having such a ghastly time because Margaret Thatcher drove him mad by ringing him up every day and telling him what to do.”
Lady Trumpington declined to identify any PM she had known who should not have had the job but when asked to name the most effective commented: “Sometimes Margaret Thatcher was great. At other times she was dreadful.”
Lady Thatcher had also “used” the peeress as a sounding board to hear other opinions “because she knew that I would argue with … anything she said that I didn’t agree with”.
Lady Trumpington also described how when she was a wartime teenage land girl on philandering former Liberal PM David Lloyd George’s farm in Surrey, “he liked measuring me… pretty well all (of me)… he had a tape measure”.
She agreed such intimate behaviour would not be tolerated today “but I thought ‘that’s what people do'”.
Born into a wealthy family which lost all its money in the Wall Street crash, Baroness Trumpington, born Jean Alys Campbell-Harris, was a cypher clerk at the Bletchley Park World War 2 code-cracking centre and went on to be a local councillor.
She joined the House of Lords in Mrs Thatcher’s first honours list, in 1980 and served as a junior and middle-ranking minister.
She came to wider public prominence in 2011 after being filmed putting two fingers up at Tory colleague Lord King when he made a reference in a Lord debate to WW2 veterans getting “pretty old”.
She retired this year from the House of Lords when she turned 95.