He was born David Ian Jackson on August 11, 1954 (not 1955, as some references mistakenly state) in Burton-upon-Trent, Staffordshire, England. His parents had met when his father was in the Navy and his mother was working in her family's pub in Portsmouth on the south coast of England. They initially settled in his father's hometown, Swadlincote, on the border of Staffordshire and Derbyshire, but when Jackson was a year old, they moved back to his mother's hometown, and he was raised in Portsmouth and nearby Gosport. His father, Ronald Jackson, became a plasterer.
Growing up in working-class poverty, Jackson was a sickly child, afflicted with asthma, first diagnosed when he was three and producing attacks that lasted into his twenties. Prevented from playing sports, he turned to books and eventually music. At 11, he began taking violin lessons, later studying timpani and oboe at school. His parents got him a secondhand piano when he was in his early teens, and he began taking lessons, soon deciding that he wanted to be a composer when he grew up. He played percussion in a citywide student orchestra. But his social milieu was more accepting of different forms of popular music than it was of the classics, and he developed a taste for that, too. Becoming interested in jazz, he formed a trio and, at the age of 16, began playing piano in a pub, his first professional gig.