Primrose was born in Glasgow and studied violin initially. In 1919 he moved to study at the then Guildhall School of Music in London. On the urging of the accompanist Ivor Newton, Primrose moved to Belgium to study under Eugène Ysaÿe, who encouraged him to take up the viola instead. In 1930, he joined Warwick Evans, John Pennington, and Thomas Petre as the violist in the London String Quartet. The group dissolved in 1935. In 1937, he began playing in the NBC Symphony Orchestra under Arturo Toscanini. When it was rumored that Toscanini would leave the Symphony in 1941, Primrose resigned. His career as a soloist took off when he started touring with Richard Crooks. He later signed with Arthur Judson, an influential concert manager. In 1946, he was the soloist in the first recording of Berlioz's Harold in Italy.
In 1944 he had commissioned a viola concerto from Béla Bartók. This was left incomplete at Bartók's death in 1945, and had to wait four years for its completion by Tibor Serly. Primrose was the soloist in the world premiere performance of the concerto, on 2 December 1949.
In 1953 he was made a Commander of the Order of the British Empire (CBE) by Queen Elizabeth II.
Primrose was known for his tremendous technique. When he performed Paganini's violin caprices on viola, Mischa Elman is said to have exclaimed, "It must be easier on viola!" Primrose wrote many transcriptions and arrangements for viola, often technically dazzling, including "La Campanella" (from Paganini's second violin concerto) and the famous Nocturne from Borodin's second string quartet, the latter "out of jealousy" for the cello's long melodic lines.
William Primrose died from cancer in Provo, Utah on 1 May 1982. His large collection of annotated viola scores became the nucleus for the William Primrose International Viola Archive at the Harold B. Lee Library, Brigham Young University. For his contribution to the recording industry, Primrose has a star on the Hollywood Walk of Fame at 6801 Hollywood Boulevard in Los Angeles.
Later in his life, Primrose became a noted teacher, writing several books on viola playing and teaching widely in Japan, Australia (where Richard Tognetti was one of his students) and the USA, occasionally at the University of Southern California (with Jascha Heifetz), the Juilliard School, Eastman School of Music, Indiana University Jacobs School of Music, Brigham Young University, and the Curtis Institute of Music. Some of his notable students include Canadian violinist Albert Pratz, former principal of the Los Angeles Philharmonic Alan de Veritch, Los Angeles Philharmonic violist Jerry Epstein, and Olympic Music Festival founder and violist Alan Iglitzin. In 1972, he published his memoirs, A Walk on the North Side.
The Primrose International Viola Competition, created in 1979 in honor of William Primrose, was the first international music competition for viola players.
The Primrose Amati viola 
For the first part of his career, Primrose played an Amati viola, formerly owned by his father. The ex-Primrose Amati is now owned by Roberto Díaz, who is currently the president of the Curtis Institute of Music and recorded a CD of Primrose's transcriptions for Naxos Records. Prior to the recording, the viola was inspected and was found to have had adjustments of questionable workmanship, which were subsequently repaired. Primrose had noted that the viola had a wolf tone and did not project easily. He was also known to have owned and played on at least one viola by William Moennig Jr. of Philadelphia.
The Primrose Guarneri viola 
In 1951 Primrose sold his Amati viola and in 1954 he purchased the 1697 ex-Lord Harrington Guarneri viola now known as the ex-Primrose. This viola is one of three known Guarneri family violas. It bears an original label of Andrea Guarneri who died in 1698 but experts believe that the work is that of his son Joseph Guarneri 'filius Andrea' who inherited his father's workshop. The ex-Primrose Guarneri is now owned by Ulrich Fritze who has played the viola during his 30 year tenure as principal violist of the Berlin Philharmonic.
- The Art and Practice of Scale playing on the Viola
- Technique is Memory. A method for violin and viola players based on finger patterns, etc.
- Walk on the north side: Memoirs of a violist
- Dalton, David (Spring 2004). "Celebrating 100 Years: William Primrose's Life and Career". Journal of the American Viola Society 20 (1): pp.13–17. Retrieved 2006-10-08.
- Terry King, Gregor Piatigorsky: The Life and Career of the Virtuoso Cellist. Books.google.com.au. Retrieved 2012-08-20.
- Classical Archives quote (All Music Guide): In the last year of his life Britten ... kept a promise made to Cecil Aronowitz ... and wrote a version of Lachrymae with an ... arrangement for string orchestra.
- "The Backyard Stories". ABC. 2007-03-09. Retrieved 2012-08-20.
- "page on Primrose's inherited Amati". Cozio.com. Retrieved 2012-08-20.
- "William Primrose (b1904; d1982), Scottish, Violist". cozio.com. Retrieved March 3, 2012.
- http://Giuseppe_%27%27filius_Andrea%27%27_Guarneri[dead link]
- Bein, Robert (1983). The "Primrose": Andrea Guarneri Cremona, 1697. Chicago, Illinois: Bein & Fushi.
- "ID: 2314". cozio.com. Retrieved March 3, 2012.
- An article on Primrose from BYU Magazine
- Primrose Archive at Brigham Young University
- AVS.htm William Primrose's Discography