Yet Number 10 aides retained doubts about whether the railwayman's son and self-made millionaire was ready to hold one of the great offices of state.
David Wolfson, Baroness Thatcher's chief of staff, wrote to her in a memo ahead of the reshuffle: "Cecil would be in a position of immense power, and you must judge whether he has yet proved himself as a Cabinet minister."
However, plans to give Lord Parkinson one of the top jobs in the government were thrown into chaos when he told Baroness Thatcher about his long-running affair with his Commons secretary, Sara Keays, on June 9, 1983.
Later that day or the following day, the prime minister received a letter from Miss Keays's father, Colonel Hastings Keays, revealing that his daughter was pregnant.
Baroness Thatcher replied tersely: "I understand that you have since spoken to the person concerned."
A draft shows that she removed a reference to returning Col Keays' letter at his request as she in fact decided to burn it in a fireplace at Chequers.
The bombshell revelations meant that Baroness Thatcher's plans for the new Cabinet had to be torn up and the reshuffle was apparently put back a day, according to the documents, released by the Margaret Thatcher archive at Cambridge University's Churchill College.
Lord Parkinson came near the bottom of a hurriedly-compiled revised list of ministers, a sign that he was no longer considered one of the government's stars.
The printed document lists him as industry secretary, although a handwritten note shows that Baroness Thatcher added the department of trade to his responsibilities as an afterthought. Geoffrey Howe was given the Foreign Office.
Nonetheless the prime minister retained great fondness for Lord Parkinson, writing a warm letter of thanks to him five days after she learned of his affair without making any reference to the matter and the problems it had caused her.
"Throughout the past two years you have given me invaluable advice, and I want to thank you most warmly for your reassurance, wise counsel and encouragement," she said.
However, the scandal reached the front pages of national newspapers in early October and Lord Parkinson resigned from the Government within days, although he stayed with his wife, Ann.
Baroness Thatcher's papers include the errant minister's resignation letter and the prime minister's reply. These were seemingly intended to be released to the press, but were never published, possibly out of concerns that they would have provided fuel to keep the story going.
Lord Parkinson wrote: "I deeply regret that by my behaviour I have caused you embarrassment and distress. I thank you for your kindness and support to us all. Ann and I have rediscovered how much we love each other and our marriage is firm."
Baroness Thatcher replied: "I am saddened beyond words both by the loss of your contribution as a member of the Government and by the tragic circumstances in which that loss has come about."
Handwritten corrections on a draft of the letter show that she paid close attention to the wording, replacing the phrase "I am strengthened by the thought that we shall remain friends" with "I am cheered by the thought that we shall see you both often".
Miss Keays gave birth to Lord Parkinson's daughter, Flora Keays, on New Year's Eve 1983.
The child was later diagnosed with learning disabilities and Asperger's syndrome, and had an operation to remove a brain tumour when she was four.
Miss Keays said that Lord Parkinson proposed to her twice but changed his mind both times. The disgraced Cabinet minister obtained an almost unprecedented court injunction banning anyone from speaking publicly about Flora or revealing her identity.
The court order expired when Flora turned 18, and in 2002 she gave a number of interviews in which she said she had missed knowing her father while growing up.
She said: "If he loved me, he would want to see me and be in my everyday life. I think my father has behaved very badly towards me."
Lord Parkinson stood down from the House of Commons and was elevated to the House of Lords in 1992 before becoming Conservative Party chairman again in 1997 for a year.
Chris Collins, a historian for the Margaret Thatcher Foundation, who has studied the private papers closely, said that making Lord Parkinson foreign secretary in 1983 would have effectively anointed him as Baroness Thatcher's choice for the next Tory leader.
"It's only speculative that she considered him to be her successor but it would appear that she was very serious about him indeed," he said.
"He had certainly risen very fast and she knew that by promoting him in this way, she would create an atmosphere around him."
A selection of the documents can be read at www.margaretthatcher.org