Wick was born in Chelmsford, Essex and attended King Edward VI Grammar School. He taught himself trombone from the age of 10 when he received an instrument from the local Salvation Army band. He played with the band until the age of 15 and soon joined Luton Brass Band which was enjoying considerable national success at the time. At the age of 16 he heard his first orchestral concert, and Malcolm Arnold's trumpet playing so inspired him, he decided to pursue a career in playing.
His family was not well off, so in an unusual step at that time, his mother started work to fund his studies. He spent a year at the Royal Academy of Music from 1950, but claims he was frustrated with not learning anything there. Sid Langston was the professor, but he all but refused to pass on any of his experience in case his students 'stole' his work.
Wick did an amateur date in Salisbury and by chance the other trombonists were from the Bournemouth Symphony Orchestra, so when the 2nd trombone job came up in May 1951, they called to invite him to audition by telegram, along with all the final year students at the London music colleges. Wick won this audition and entered this large full-time professional orchestra at the age of 19. He went on to win an audition with the City of Birmingham Symphony Orchestra in 1952, a year after conductor Rudolf Schwarz had moved there. The audition had to be stern to persuade the administrators that he wasn't handing out jobs to his friends.
In Birmingham in 1955 Wick worked with Gordon Jacob in premiering the famous trombone concerto. This piece shows off the advances in technique that he was making: the cadenza in the last movement makes great use of warm-up and flexibility studies that Wick had developed and would prove hugely influential in the teaching of brass players in Britain to this day.
It was his position as principal trombone at the London Symphony Orchestra (LSO) 1957-1989 for which he is most revered, especially as they made so many fine recordings. The brass playing in the Star Wars films has encouraged a whole generation of brass players, Wick making a blistering sound in partnership with another legend, Maurice Murphy, on 1st trumpet. Another recording where Wick made his mark is in the large solo in the 1970 LSO/Horenstein (Unicorn) recording of Mahler's Third Symphony.
Soon after moving to the LSO, Denis moved the LSO section from .485" bore Boosey Imperial tenor trombones and a .523" G bass trombone to the American "large bore" instruments (.547" tenor and slightly larger bass, now in B♭). Experimentation possibly started in Birmingham, and the Jacob Concerto suits the larger sound, but post-war import restrictions made these instruments impossible to obtain legally before 1958. Certainly he was a pioneer in Britain, and soon all the other orchestral players followed suit.
Wick taught initially at Guildhall School of Music and Drama (1967-1976) and since 2000 has served on the faculty at the Royal Academy of Music, London. He also works with the Gustav Mahler Youth Orchestra. He has his own line of mouthpieces and mutes for brass instruments, made by Denis Wick Products Ltd, and owns Denis Wick Publishing.
He has been honoured by the International Trombone Association several times. In 1989 he was awarded the ITA Award, presented each year to an individual who has greatly influenced the field of trombone. And in 2006 he was presented with the Neill Humfeld Award, which recognizes outstanding trombone teaching. During his Presidency of the ITA 2004-2006 he brought the International Trombone Festival to Birmingham, and made great strides to internationalize the magazine.