Speaking on This Morning on Monday, the 90-year-old recalled the first time she ever met Princess Margaret.
“I was three, she was five, and the minute I saw her, I knew she was my type of friend,” she said.
“I remember we were tricycling around the marble hall, and the Queen came downstairs and said, ‘Anne and Margaret, what are you doing!’
“The Queen was always looking after Princess Margaret - she was a wonderful sister,” she added.
Her comments come as her second memoir Whatever Next? Lessons From An Unexpected Life is set to be published, a book she said she wrote because there was still “so much more” to say about her relationship with the royal family.
“The reason I wrote another book was because there was so much I left out of Lady in Waiting,” she explained.
“I was so angry, because a book had been written about Princess Margaret which was so untrue, so I wanted to write one… she was a great friend to me.”
She said: “I’m devoted to King Charles… I think the coronation will be much smaller, I don’t think there’ll ever be a coronation like the one I took part in.
“It was just after the war and I think that made a difference. Suddenly, this explosion of colour.”
She recalled carrying the future queen’s train as they prepared to leave for the coronation when she “looked round suddenly and said, ‘Ready girls?’”.
In the book, Lady Glenconner also opens up about the domestic violence she suffered at the hands of her husband, Colin Tennant, revealing that he once beat her so badly that she permanently lost the hearing in her ear.
Early on in their marriage, which began in 1956, he told her: “I'm going to break you, Anne.”
In an extract from her new book published in the Daily Mail, she adds: “He failed to do so, and he was proud of me for that. He said to me another time: 'I knew you'd be able to take it.'”
She added that, particularly in the early years, he “almost destroyed me”.
Anyone who requires help or support can contact the National Domestic Abuse Helpline which is open 24/7 365 days per year on 0808 2000 247 or via their website https://www.nationaldahelpline.org.uk/