The newspaper said the Queen’s political views were made known in several briefings by her advisers, who were aware the information would be published.
Under Britain’s constitution, the monarch must be non-political.
This meant such a revelation of the Queen’s feelings threatened the confidentiality she had maintained for decades.
In the interview released this week, Mr Neil claimed royal aides were “prepared to lie” when it was in their interest to do so.
He said: “It taught me that when their backs are up against it they were prepared to lie, but it also taught me they were not very agile in dealing with a bushfire that threatened to turn into a forest fire.
“They were slow to react, they were not used to being in the frame in this way.”
Andrew Neil news: Neil said the Queen was ‘upset’ with his story
Andrew Neil news: The Sunday Times ran the story on Thatcher’s feud with the Queen
Mr Neil was asked about the story published by the Sunday Times.
Mr Rajan said: “You managed to, with a single story, infuriate the Queen, Rupert Murdoch and Margaret Thatcher.
“It had the immortal headline ‘Queen dismayed by ‘uncaring’ Thatcher’, how did you get away with that?”
Mr Neil responded: “Well I almost didn’t get away with it. It’s not a great move to manage to upset the two most powerful women in the country, the Prime Minister and the Queen.
“I got away with it in the end because the story was true, and I got away with it because Rupert Murdoch stood by me.
Andrew Neil news: The Queen Mother with Thatcher in 1980
“That was one of the advantages of having a proprietor that had no interest in social advancement in London society.”
While at the BBC, Mr Neil was not able to voice his own political opinions due to impartiality rules, but will have more freedom now he has left.
He discussed his views on the Royal Family in the interview, revealing his “biggest objection” to the monarchy.
Mr Rajan also pointed out that, in 1997, Mr Neil argued the republican side in a debate and asked whether he still held republican views.
Mr Neil replied: “Not really.
Andrew Neil news: Neil said he had objections to the Royal Family
Andrew Neil news: He alleged that Buckingham Palace tried to have him sacked
“I am not a cheerleading monarchist, I can see the strength of a republic.
“My main objection to the Royal Family at that time was basically Marxist.
“It behaved like it was the pinnacle of a class system, and they were the top ones.
“My Sunday Times was devoted to breaking up Britain’s class system, and I thought it would be possible to have a Royal Family separate from the class system.”
Source: EXPRESS CO UK