Born in 1921 in London to an English father, John Nearne, and Spanish mother, Marie de Plazoala, she was the youngest of four children. Her elder sister, Jacqueline Nearne, and one of her two brothers, Francis, would also become SOE operatives.
In 1923, the family moved to France, where Nearne became fluent in French. The two young women made their way to London via Barcelona, Madrid, Lisbon, Gibraltar and Glasgow, while the rest of the family remained in Grenoble, despite the German invasion of the country. On her arrival in England she was offered service in the WAAF working on barrage balloons, but turned this down and was recruited by the SOE. Initially Nearne worked as a home-based signals operator, receiving secret messages from agents in the field, usually written with invisible ink on the back of typewritten letters. Her sister Jacqueline was sent to France to work as a courier. The sisters were supposed to keep their roles secret from one another, but were unsuccessful.
She was flown by a Lysander aircraft to a field near Les Lagnys, Saint-Valentin in Indre, France, in the late hours of 2 March and the early hours of 3 March 1944 with Jean Savy to work as a wireless operator for the Wizard network as part of Operation Mitchel. Her cover story was that she was Mademoiselle du Tort (also using the aliases Jacqueline Duterte and Alice Wood). Using the code name "Rose", she was given the mission of helping Savy set up a network in Paris called "Wizard"; its aim, unlike the networks dedicated to sabotage, was to organise sources of finance for the Resistance. Nearne's role was to maintain a wireless link to London, and in the course of the next five months she transmitted 105 messages.
Savy had returned to London with important information about German V1 rockets, leaving Nearne on her own. Although she did not know it at the time, the same aircraft which took Savy home also carried her sister, Jacqueline, who had just completed 15 months in the field. Nearne then worked for the "Spiritualist" network.
In July 1944 her transmitter was detected and she was arrested. Nearne "survived, in silence, the full revolting treatment of the baignoire" in the torture chamber of the Paris headquarters of the Gestapo on the Rue des Saussaies.
She reportedly managed to convince her captors, under torture, that she had been sending messages for a businessman, unaware that he was British. On 15 August 1944, she was sent to Ravensbrück concentration camp where she refused to do prison work. Her head was shaved and she was told she would be shot if she continued to refuse. She was then transferred to a forced labour camp in Silesia. While in one of these prisons she was reportedly tortured.
On 13 April 1945 she escaped with two French girls from a work gang by hiding in the forest, later travelling through Markkleeberg, where they were arrested by the S.S. but released after fooling their captors and reportedly hidden by a priest in Leipzig until the arrival of United States troops.
After World War II, she was awarded the Croix de Guerre by the French government. On 19 February 1946 she was appointed a Member of the Order of the British Empire (MBE) by King George VI for services in France during the enemy occupation.
After the war Nearne lived in London with her sister, Jacqueline, where, The New York Times reported, she suffered from "psychological problems brought on by her wartime service". After her sister's death in 1982, she moved to Torquay and lived there quietly until her death. She died alone from a heart attack in her seaside flat. Her body is thought to have remained undiscovered for some time until found on 2 September 2010. She was 89 years old. Nearne talked about her wartime activities on a Timewatch television documentary in 1997, but she wore a wig, and spoke in French under her codename "Rose", and her wartime activities were not generally known about. It was only when her flat was being searched by council workers to try to establish her next-of-kin that medals and other papers related to her war career were found.
Her next of kin, a niece, was located living in Italy and has said she was upset that Nearne had been portrayed as being "alone or unloved", adding, "Although I don't live in the UK, I was very close to Aunt Eileen and visited her often. I only saw her six months ago. She was always cherished by the family."
Nearne's funeral, which was provided free of charge by the Torbay & District Funeral Service of Torquay, was held on 21 September 2010 at Our Lady Help of Christians and St Denis Roman Catholic Church, Torquay. The eulogy was made by Adrian Stones, Chairman of the Special Forces Club. Her body was cremated, and her ashes scattered at sea, according to her wishes. Nearne died intestate and her estate of around £13,000 went to her niece in Tuscany, Italy, according to BBC One's program Heir Hunters; series 6, episode 1.