They say Mrs Thatcher is said to have responded "explosively" after being told that there would not be room for her in the cathedral's crypt for the 1985 unveiling by the Queen.
The exchange of letters and memos, released by the Margaret Thatcher Archive Trust, suggests that with the limited space and large number of clerics and royals it would not leave any space for politicians.
This is reported to have followed a high profile falling-out between Mrs Thatcher and the then Archbishop of Canterbury, Robert Runcie.
Thatcher criticised him over a perceived lack of patriotism in praying for the Argentinian dead in a 1982 memorial.
One aide wrote in a memo: "My first reaction was that it was very curious not to suggest the PM be at the unveiling of the plaque.
"At the same time there would be four Chiefs of Staff present, and the clergy, by subtraction would amount to 13 in number."
Thatcher's Principal Private Secretary Robin Butler intervened, writing on the note: "Let me have a word. I think that the PM should be present at the unveiling," after feeling that Mrs Thatcher would not be happy with the decision.
It is then thought the then Defence Secretary, Michael Heseltine, allowed the letter to reach the Prime Minister showing him signing off the arrangement.
According to Chris Collins, the only historian to have studied to papers, she responded "explosively" scrawling on the letter: "Kindly ask the secretary of state to see me immediately." The word "immediately" was underlined twice.
Defence Secretary, Mr Heseltine later apologised for his involvement, sending a polite apology reading: "I am satisfied that this matter was not well handled."
Mr Collins commented that: "Mrs Thatcher's private office was paying close attention to the arrangements in part because the Archbishop of Canterbury was preaching and memories of the 1982 service of thanksgiving had not faded.
"It had not initially seemed like a problem until the cathedral authorities hit upon the idea that they needed an extraordinary number of clerics to be present.
"They cited protocol and the ecclesiastical equivalent of crowd control - a big contingent of vergers being necessary to keep a procession like this from getting lost on the way to the crypt.
"The suspicion has to be there that they hit upon a scheme to prevent her taking over due to some natural sense that it was their place to organise the ceremony and it shouldn't become some kind political rally."
These letters do not clarify whether a solution was reached or whether Lady Thatcher was present for the unveiling.
But Mr Collins said: "It seems likely that they discovered the crypt was a little larger than they originally thought and managed to squeeze a Prime Minister and a leader of the opposition in."
