Morison was born in Ballarat, Victoria, and studied at the Melbourne Conservatorium of Music from 1943-45. Her teachers included Clive Carey, with whom she continued studies at the Royal College of Music 1947-1948.
Morison made her English concert debut at the Royal Albert Hall in Handel's Acis and Galatea in 1948 and that autumn joined Sadler's Wells Opera, appearing regularly there until 1954. She sang Anne Trulove in the first British staging of Stravinsky's The Rake's Progress in 1953 in Edinburgh, and at her Glyndebourne debut the following year. After a notable Covent Garden debut in 1953 as Mimi in Puccini's La bohème, she sang there regularly until 1962. She was admired for the touching sincerity of her acting and the lyrical warmth of her voice, in such roles as Susanna (The Marriage of Figaro), Pamina (The Magic Flute), Marzelline (Fidelio), Micaela (Carmen), Antonia (The Tales of Hoffmann), Marenka (The Bartered Bride), and Blanche in the British premiere of Poulenc's Dialogues of the Carmelites in 1958. In 1955 she created the title role of Arwel Hughes's Menna for the Welsh National Opera.
In 1955, she received the Portuguese Order of Public Education.
She has appeared as an oratorio singer in Denmark, the Netherlands, France and the United Kingdom.
Among Morison's many recordings, those of Purcell, Handel and Michael Tippett's A Child of Our Time capture the grace and conviction of her singing. She has also recorded an outstanding and very well received complete Brahms Liebeslieder Waltzes, Opp. 52 and 65, with Marjorie Thomas, Richard Lewis and Donald Bell, accompanied by Vitya Vronsky and Victor Babin.
- Rosenthal, Harold (1992), 'Morison, Elsie' in The New Grove Dictionary of Opera, ed. Stanley Sadie (London) ISBN 0-333-73432-7
- Warrack, John and West, Ewan (1992), The Oxford Dictionary of Opera, 782 pages, ISBN 0-19-869164-5