Moore was born the son of a railway electrician in Dagenham, Essex, England. His working-class parents showed little affection to their offspring (as his older sister publicly revealed).

He was notably short: 5' 2½" (1.59 m) and was born with a club foot that required extensive hospital treatment and which, coupled with his diminutive stature, made him the butt of jokes from other children. Seeking refuge from his problems he became a choirboy at the age of six and took up piano and violin.

He rapidly developed into a very talented pianist and organist and was playing the pipe organ at church weddings by the age of 14. He attended Dagenham County High School where he received musical tuition from a dedicated teacher, Peter Cork. Cork became a friend and confidant to Moore, corresponding with him until 1994.

His musical talent won him a scholarship to Magdalen College, Oxford and whilst studying music and composition there, he performed with Alan Bennett in the Oxford Revue. Bennett then recommended him to the producer putting together Beyond the Fringe, a comedy revue, where he was to first meet Peter Cook.

Beyond the Fringe was at the forefront of the 1960s satire boom and after enormous success in Britain, it transferred to the USA where it was also a major hit.

During his university years, Moore took a great interest in jazz and soon became an accomplished jazz pianist and composer, as well as working with such leading musicians as John Dankworth and Cleo Laine.

In 1960, he left Dankworth's band to work on Beyond the Fringe. During the 1960s he formed the acclaimed "Dudley Moore Trio" (with drummer Chris Karan and bassists Pete McGurk and later Peter Morgan). Moore's admitted principal musical influences were Oscar Peterson and Errol Garner.

In a later interview he recalled the day he finally mastered Garner's unique left hand strum, and he was so excited he walked around for several days with his left hand constantly playing that extraordinary cadence. His early recordings included "My Blue Heaven", "Lysie Does It", "Poova Nova", "Take Your Time", "Indiana", "Sooz Blooz", "Bauble, Bangles and Beads", "Sad One for George" and "Autumn Leaves".

The trio performed regularly on British television, made numerous recordings and had a long-running residency at Peter Cook's club, The Establishment.

Moore composed the soundtracks for the films Bedazzled, Inadmissible Evidence, Staircase, and Six Weeks, among others.

In the early 1970s, he had a brief relationship with British singer-songwriter Lynsey De Paul, whom he met at a party.