Born in Nottingham in 1938, David would study at its College of Arts in the late 1950s already demonstrating a predilection for bold, abstract work. In 1961 he would move to London to complete his training with a further three years study at the Royal Academy, immersing himself in nascent movements of the 1960s such as from Pop Art to Op Art. Upon graduation, Leverett began exhibiting almost immediately with a series of shows at the Redfern Gallery, followed by one shows at the John Moores Liverpool Exhibition in 1967 and the Whitechapel Art Gallery in 1968. In the same year, still only thirty, his work was included at the RA Bicentenary Exhibition.

Leverett’s work is emblematic of the avant-garde 1960s British art scene. With its large scale and irregularly shaped geometry, captured in vivid acrylics, Leverett’s paintings appear highly energetic and dynamic. In his later years, he would begin to pull back slightly from abstraction, producing bold landscapes that reflect a growing concern with environmental causes. While he was perhaps best known for the work he produced in the sixties, he continued to remain an important force in British art, winning the inaugural Sargant fellowship at the British School in Rome in 1990.

Alongside his painting, David was for many years a leading teacher at the Slade School of Fine Art, a role for which he is fondly remembered by numerous students. Education was clearly a passion of his, and in addition to his work at the Slade David would often travel internationally to give workshops. David passed away in 2020 at his Kentish Town home after a career of over fifty years. During that time his work had been shown around the world, from Venice to New York and today his paintings are in multiple museum collections, most importantly at Tate Modern.