Lady Elizabeth Cavendish, who has died aged 92, was the daughter of the 10th Duke of Devonshire, a childhood friend of the Queen, a lady-in-waiting to Princess Margaret and, famously, the long-standing companion and soulmate of the Poet Laureate John Betjeman.

They met in 1951 at a dinner in Mayfair given by Lady Pamela Berry. Dinner was delayed when one of the guests, Guy Burgess, failed to attend, having just defected to Moscow. Though the willowy Lady Elizabeth was some 20 years younger than Betjeman (and taller), and he was already married to his wife Penelope, as Betjeman’s daughter Candida Lycett Green put it, Elizabeth became his “beloved other wife”. Unflatteringly, he nicknamed her “Feeble”; in fact, though ostensibly rather shy, she was anything but.

For some 30 years until his death in 1984, Lady Elizabeth’s mother’s house at Edensor on the Chatsworth estate became the poet’s second home. Penelope knew about Elizabeth, but neither woman wanted to force the issue. Betjeman told friends he felt torn between the two, but could give up neither.

Their relationship remained an open secret among friends until 1973 when Betjeman – now Sir John, the Poet Laureate – moved with his wife to a house five doors away from Lady Elizabeth in Radnor Walk, Chelsea, and their ménage à trois was suddenly all over the media.

Lady Elizabeth never married and always refused to discuss her relationship with Betjeman. She did not cooperate with his daughter, Candida, when she edited and published her father’s letters in 1995, and she also declined to help Bevis Hillier, Betjeman’s official biographer.

Their letters to each other have been placed under embargo until 2034. So the precise nature of their friendship remains a matter of some speculation – there have even been suggestions that it may always have been platonic, though that seems unlikely.

Bevis Hillier claimed that “when John was with Elizabeth, she ministered to his comfort in a way that Penelope rarely did”, and in a 2001 interview in a BBC Two documentary Lady Wilhelmine Harrod, who had been briefly engaged to Betjeman, spoke of a letter she had received from the poet in 1974.

“I have lived so long apart from Penelope, that Elizabeth now loves me more than anybody else in the world,” wrote Betjeman. “I depend on Elizabeth for food for my body and mind … Elizabeth has given up marriage and a family with her own children out of love for me.”

In fact, as revealed much later, the ménage à trois was, for many years, a ménage à quatre. In a 2007 article in The Spectator Andrew Geddes claimed that throughout the 1960s and 1970s Betjeman had a third girlfriend, Andrew’s mother Margie Geddes.

According to Andrew Geddes’s account, the sexual element of Betjeman’s relationship with Elizabeth, if there had been one, had cooled by the early 1970s: “One day in the early 1970s John and Penelope unexpectedly came to tea … Penelope stayed on after John had left. ‘She talked of Feeble … with some sadness,’ my mother recorded. ‘It’s the eternal triangle, Margie,’ she said, ‘but I don’t think there is any sex in it, he is past that now.’ Mother, perhaps wisely, kept her counsel. Afterwards she told us, ‘ … Feeble was his great love. She looked after him devotedly, but when I knew him it seemed he no longer desired her’.”

Geddes recalled an occasion when Betjeman rang Margie in a panic because he could not get his front door key to work to leave the house. Margie went round to his house, and after persuading him to pass the key through the letterbox, opened the door from the outside.

“He flung himself into her arms. ‘You’ve saved me,’ he cried, ‘oh thank you, thank you.’ At that moment Feeble walked up the street. She said nothing, but a few minutes later the telephone rang and her peremptory voice could be overheard to say, ‘You’ve got to get rid of that woman at once.’ He protested, but then turned to Mother almost in tears and, giving the impression of a small boy being summoned by the headmaster, he said, ‘I’ll have to go to her’, and, abject and visibly shaking, he left.”

Yet Betjeman’s letters also reveal the fun, and intellectual companionship, which his relationship with Lady Elizabeth Cavendish afforded him. She was a highly intelligent woman and, like him, a strong Anglican. He is said to have told friends that without her he would never again write anything of consequence. Moreover, as the daughter of a duke and part of the royal circle, she also appealed to his social aspirations.

When Betjeman’s London flat was damaged by fire he moved into a Rotherhithe flat owned by Antony Armstrong-Jones, whose friendship with Princess Margaret (to whom he had been introduced at one of Lady Elizabeth’s dinner parties), was just beginning.

When Betjeman was awarded the Duff Cooper prize for his Collected Poems in 1958, the presentation was made by the princess, whose speech, referring to the recipient as “a friend of mine”, moved him to tears.

Maurice Bowra, who chaired the judges, was prompted to pen the mock-Betjeman verse: “Green with lust and sick with shyness, Let me lick your lacquered toes. Gosh, O gosh, your Royal Highness, Put your finger up my nose …”

In April 1984, the poet spent Easter with Lady Elizabeth at Chatsworth and he died a month later in Cornwall, with her by his side. He was buried there, and the long-suffering Penelope had to rush down from London for the funeral. Those attending the occasion found it rather awkward.

Elizabeth Georgiana Alice Cavendish was born on April 24 1926, three days after Princess Elizabeth, the fourth of five children of Edward Cavendish, Marquess of Hartington, then an MP, later the 10th Duke of Devonshire. Her mother, Lady Mary Gascoyne-Cecil, would become the first chancellor of the University of Exeter and Mistress of the Robes, the most senior of the Queen’s ladies-in-waiting.

Lady Elizabeth was educated by governesses and became a close childhood friend of the young princesses. She and Princess Elizabeth were both members of the Girl Guide company at Buckingham Palace, and from 1951 until 2002 she was a lady-in-waiting to Princess Margaret, accompanying her on overseas visits.

According to AN Wilson, Lady Elizabeth Cavendish was “naturally drawn to a bohemian life”. Lucian Freud asked her to sit for him in 1950 (she agreed on condition that she would not have to have the picture).

However, although it was through her that Princess Margaret met Antony Armstrong-Jones, she was horrified when the princess told her of their engagement. According to the princess’s official biographer, Christopher Warwick, Lady Elizabeth asked her friend: “Are you sure you’re able to put up with his bohemian way of life?”. “By ‘bohemian’ I think Lady Elizabeth was using an umbrella term covering all aspects of his life as she knew it,” Warwick said. “She was a very great friend of his, remember, and certainly knew that he had lots of gay and bisexual friends who went to his parties in Pimlico.”

Lady Elizabeth Cavendish remained totally discreet and loyal to both the Queen and her sister. In 1996, when she was granted royal permission to talk to Ben Pimlott for his biography of the Queen, she contradicted claims that the Queen had been an unfeeling mother to her eldest son: “It simply isn’t true that she neglected Prince Charles,” she said. “I stayed at Sandringham a lot during those early years, and she wasn’t at all chilly with him. She used to come to picnics where he was the centre of attention. She adored him.’’

From childhood, encouraged by her maternal grandmother, Alice, Marchioness of Salisbury, Lady Elizabeth developed a keen sense of public good and concern for the less privileged. In 1954 a newspaper reported that “she does welfare work in London’s East End and her duties there, helping with the baby, talking sense into a juvenile delinquent, come before the pleasures of society.”

A magistrate from 1961, she served in the 1980s as chairman of North Westminster magistrates and of Inner London Juvenile Courts. She also spent 10 years as a member of the Advertising Standards Authority, was chairman of the Cancer Research Campaign (1981-96) and a lay member of the Bar Council. During the 1990s she was also on the council of St Christopher’s Hospice, Sydenham, and a member of the Press Complaints Commission.

She retired permanently to Edensor, where she lived with her Jack Russell, Sally, and enjoyed sewing tapestries. In old age she was particularly close to her sister-in-law Debo, Duchess of Devonshire.

She was appointed LVO in 1976 and promoted to CVO in 1997.

Lady Elizabeth Cavendish, born April 24 1926, died September 15 2018