Kretzmer was born in Kroonstad, South Africa, in 1925. He is one of four brothers of Lithuanian Jewish immigrants William and Tilly Kretzmer, who fled the pogroms of Czarist Russia to settle in small-town South Africa early in the 20th century. His parents ran a furniture store. Elliot, the oldest of the brothers, flew as part of a bomber crew in the South African Air Force during the second World War, eventually becoming the Mayor of Johannesburg in 1991.
Kretzmer began his professional career writing documentary films and the commentary for a weekly cinema newsreel. However, he soon moved on to print journalism, initially as a reporter and feature writer for the Johannesburg Sunday Express. He relocated to London in the mid-1950s and pursued twin careers as journalist and lyric writer.
After several years as a feature writer on the Daily Sketch, Kretzmer became a profile writer on the Sunday Dispatch and the Daily Express, interviewing John Steinbeck, Truman Capote, Tennessee Williams, Sugar Ray Robinson, Louis Armstrong, Henry Miller, Cary Grant and Duke Ellington. In 1962, he became senior drama critic of the Daily Express: a post he held for 18 years, covering about 3,000 first nights.
From 1979 to 1987, he wrote television criticism for the Daily Mail, winning in this capacity two national press awards, including TV Critic Of The Year.
Kretzmer wrote lyrics for the BBC's satire That Was The Week That Was, including the racial satire "Song of Nostalgia For an American State" and the much-recorded tribute to John F. Kennedy, "In the Summer of His Years", written and performed by Millicent Martin within hours of his assassination.
Kretzmer won an Ivor Novello Award for the Peter Sellers and Sophia Loren comedy hit “Goodness Gracious Me”, composed by David Lee. Other award-winning Kretzmer lyrics include “Yesterday When I Was Young” and the chart-topping “She”, both written with and for the French singer Charles Aznavour..
Kretzmer wrote the lyrics for Anthony Newley’s cult musical film Can Hieronymus Merkin Ever Forget Mercy Humppe and Find True Happiness, whose score included “When You Gotta Go”, often used as a closing song by singers including Barbra Streisand.
Kretzmer wrote the book and lyrics of the West End musical, Our Man Crichton, composed by David Lee and based on J M Barrie’s satirical play The Admirable Crichton. The musical starred Kenneth More and Millicent Martin. Kretzmer later wrote (with composer Laurie Johnson) the lyrics for a large-scale comedy spoof, The Four Musketeers, which ran for more than a year at the Theatre Royal, Drury Lane, starring Harry Secombe as the swordsman d'Artagnan.
In 1985, Kretzmer’s songs for Aznavour came to the attention of producer Cameron Mackintosh, who invited him to write an English version of a French musical Les Misérables (by Alain Boublil and Claude-Michel Schonberg). Kretzmer’s lyrics extended the two-hour Paris original into a three-hour show. The all-sung “Les Mis” opened at the Barbican Theatre on 8 October 1985 and is still running in the West End, the longest running West End musical in history. The score includes such well-covered ballads as "I Dreamed a Dream", "Bring Him Home", "On My Own" and "Empty Chairs At Empty Tables". For his work on the Les Misérables lyrics, Kretzmer received Tony and Grammy awards.
In 2008 Kretzmer wrote the lyrics for Marguerite from an original text by Alain Boublil, a musical set in Nazi-occupied Paris, to music by Michel Legrand. The show was part of a Jonathan Kent Season at the Haymarket Theatre before moving on to a season in Japan. Marguerite was shortlisted in the Best Musical category in the Evening Standard Drama Awards 2008.
Kretzmer’s most recent musical project is Kristina, based on Vilhelm Moberg’s epic suite of novels about Swedish emigrants to Minnesota in the 19th century. The show, originally conceived and written by lyricist Björn Ulvaeus and composer Benny Andersson from ABBA, was presented and recorded in a concert version over two nights at Carnegie Hall, New York in September 2009.
In 1988, Kretzmer was elected a Chevalier of L’Ordre Des Arts Et Des Lettres. He received the Jimmy Kennedy Award (a division of the Ivor Novello Awards) for services to songwriting. In 1996, he was elected an Honorary Doctor of Letters at Richmond College. He was appointed Officer of the Order of the British Empire (OBE) in the 2011 New Year Honours for services to music.
He was nominated for Best Original Song at the 70th Golden Globe Awards for the song "Suddenly" from the 2012 film version of Les Miserables.
In 1961 Kretzmer married Elisabeth Margaret Wilson and they had one son and one daughter. This marriage dissolved in 1973. He married Sybil Sever in 1988.
On 8 April 2011, Kretzmer received an Honorary Doctorate from Rhodes University in South Africa.