Donald Christopher Barber was born on April 17, 1930, in Welwyn Garden City, Hertfordshire, the son of an insurance statistician and a headmistress. He started on the violin at seven, was evacuated from London during the war, and began collecting 78 rpm records of New Orleans jazz. After a grammar school in Worcestershire and then St Paul's School in London, where he began going to jazz clubs, he bought his first trombone for 5 pounds from a trombonist in Humphrey Lyttelton's band. He spent three years at the Guildhall School of Music, studying double bass, and played there with the guitarist Alexis Korner. In 1950 he formed a nonprofessional New Orleans Jazz Band, with Korner on guitar and Barber himself on bass. He had trained as an actuary, left his insurance job in 1951, and became a full-time musician the following year.

In late 1952 Barber and the clarinetist Monty Sunshine put together a cooperative band, and took on the trumpeter Ken Colyer, fresh from a stay in New Orleans, as its nominal leader. As Ken Colyer's Jazzmen, with Lonnie Donegan on banjo, Jim Bray on bass and Ron Bowden on drums, they made their debut in Copenhagen in April 1953 and recorded for the Danish Storyville label. Colyer left in 1954 after quarrels over the band's direction, Pat Halcox took the trumpet chair on May 31, 1954, and the group became Chris Barber's Jazz Band. Halcox stayed for 54 years, until July 2008. At the band's first Decca session in London on July 13, 1954, which produced the 10-inch LP New Orleans Joys, Donegan sang and played guitar on "Rock Island Line" and "John Henry" with Barber on double bass and Beryl Bryden on washboard. Issued as a single under Donegan's name in late 1955, "Rock Island Line" became a hit in 1956 and set off the British skiffle craze.

The Northern Irish blues singer Ottilie Patterson joined the band full time on December 28, 1954, and made her first public appearance with it at the Royal Festival Hall on January 9, 1955. She and Barber married in 1959. She sang with the band regularly until about 1963, retired from it officially in 1973, and returned for a series of London concerts in 1980; they divorced in 1983. The band's October 1956 recording of Sidney Bechet's "Petite Fleur", with a clarinet solo by Sunshine, was issued in 1958 and in 1959 reached number 3 in Britain and number 5 in the United States, selling more than a million copies. Barber toured the United States for the first time that year. Sunshine left in 1960, and Ian Wheeler took over the clarinet and saxophone chair.

Barber's other great project of these years was bringing American blues and gospel musicians to Britain. He booked Sister Rosetta Tharpe for a month-long British tour in 1957, and Sonny Terry and Brownie McGhee toured with his band and made the LP Sonny, Brownie and Chris on May 2, 1958. Muddy Waters toured England in 1958 backed by trad musicians including Barber and members of his band, and Barber is also credited with arranging British tours by Big Bill Broonzy, Terry and McGhee, and Waters in the late 1950s and early 1960s. Waters's electric sound unsettled much of the traditional audience but inspired younger players such as Korner and Cyril Davies to move toward electric blues, and Barber is widely counted as a significant figure in launching British rhythm and blues. In 1958 he also became a founding director of the Marquee Club in London, together with its owner Harold Pendleton, and the band was among its early resident acts. Louis Jordan toured with the band and recorded with it in 1962.

Barber kept changing the band. In 1964 he brought in the blues guitarist John Slaughter, who stayed until shortly before his own death in 2010 apart from a gap from 1978 to 1986, and a second reed player soon followed. A 1967 recording of "Catswalk", written by Paul McCartney, was released as "Cat Call", and the band signed to Marmalade in 1969. It was especially popular in Germany and Eastern Europe through the 1960s. The 1972 album Drat That Fratle Rat has Rory Gallagher on lead guitar on its title track. In 1975 the original band, with Donegan and Sunshine, reunited at Croydon; in 1976 Barber toured with the alto saxophonist Russell Procope and recorded Echoes of Ellington at St Ives on June 3, and in 1981 he toured with Dr. John. The 1979 album Swing Is Here paired him with the pianist John Lewis and the trombonist Trummy Young.

He moved into other settings late in his career. A Concerto for Jazz Trombone, co-written with Richard Hill, was premiered at the Palast der Republik in East Berlin on October 2, 1986, and in 1991 he recorded Under the Influence of Jazz with the London Gabrieli Brass Ensemble. He received the OBE that year. The band celebrated its 40th anniversary in 1994 with a tour alongside Donegan's group, and in November 1998 Barber played double bass and trombone on Van Morrison's The Skiffle Sessions in Belfast. From 1998 he enlarged the band, with the trombonist and arranger Bob Hunt, to play the music of the early Duke Ellington orchestra, and by 2001 it had become the 11-piece Big Chris Barber Band, though a New Orleans-style six-piece set stayed in each program. He received an honorary doctorate from Durham University in 2006, the Blues Louis at the Lahnstein Blues Festival in 2013, and the German Jazz Trophy in 2014, and published his autobiography Jazz Me Blues, written with Alyn Shipton, in 2014. He announced his retirement on August 12, 2019, after about 70 years of playing, and the band continued under Hunt's musical direction. Barber married four times, to Naida Lane, Patterson, Renate Hilbich and Kate Gray, and was a keen motor-racing driver. He passed away on March 2, 2021, at 90, after living with dementia.

Barber led from the trombone in the New Orleans revival style, with a six-piece lineup of trumpet, trombone and clarinet over banjo, bass and drums, but he never confined the band to that formula. It carried a skiffle spot that launched Lonnie Donegan, a deep blues and gospel repertoire, a long-running tribute to early Duke Ellington, and by the 1960s an electric guitar and a second reed player. He also took an interest in Joe Harriott, Charles Mingus and Joe Zawinul. His audience was the trad boom of the late 1950s and early 1960s, which he shared with Acker Bilk and Kenny Ball, and the tours he arranged were where many young British players first heard American blues and gospel at first hand. Donegan's skiffle was in turn an early inspiration for John Lennon and Paul McCartney. The critic Richie Unterberger rates the band's 1950s concert LPs above its stiffer studio sessions of the same years, and Bob Stanley has called Drat That Fratle Rat an unlikely but terrific trad and blues-rock hybrid.