Her father was Arthur Green, a variety performer who adopted the stage name of Tom Lenner, and toured with his wife, Florence Wright, Anne's mother.
The Lenner Sisters song and dance act ended when Ida got married and started a double-act with her new husband.
Her elder sister, Jud, paid for Lenner to have dancing lessons, so she could understudy Judy in a production showing at the Loughborough Theatre.
At another engagement in 1934, at Murray's Club in Soho's Beak Street, she was heard by Savoy Hotel bandleader Carroll Gibbons.
Gibbons was so impressed with Lenner's voice that he invited her to record with his group for a Radio Luxembourg broadcast sponsored by Hartley's Jam.
The Savoy management initially objected to the presence of a female vocalist, but Gibbons believed in Lenner and he refused to give in.
Apart from the Hartley's Jam programme, Lenner also appeared with Gibbons in the Ovaltineys, in which she became known to millions of children as "Auntie Anne".
Lenner sang with a gentle "Mayfair" accent, based on received pronunciation, and did not attempt to "project" her voice at the audience.
Her contract for the Savoy did not prevent her from recording one song with Joe Loss in 1936 or appearing with Eric Wild and his "Tea-timers", who were regularly on pre-war television from Alexandra Palace.
In the same year, she also contributed to bandleader George Scott-Wood's record "Fred and Ginger Selection" where she sang "Lovely To Look At" and duetted with Brian Lawrance on "I Won't Dance".
She was also in demand for ENSA shows and was called upon to sing at official Government functions; Lenner performed in front of Winston Churchill and General Dwight D. Eisenhower among others.
After the war, she did troop shows in Austria, Germany and Italy; one of these was with her trio, which included Spike Milligan on vocals and guitar of whom she later said: "He is a lovely man, so talented.
Her overseas work also included Monte Carlo, where she had a show at the Casino and in Paris where she sang with Bert Firman.
Her nephew, John Doyle, believed that her voice had started to fail, which may have been partly due to heavy smoking and the strain placed on her vocal cords by working without microphones during her early career.
Jeffrey found it difficult to obtain work after his return from Australia, where he had hosted his own television programme, and he was never able to emulate the success of his mother.
Around the outbreak of World War II, Lenner married for a second time, to up-and-coming actor Gordon Little, who was in the Navy, stationed at Portsmouth.
Gibbons' widow Joan recalls, "Anne was a marvellous raconteur, a very quick brain and with a strong sense of humour.