Smith studied at Sheffield College of Art (1944–1946), Saint Martin's School of Art (1948–1950) and the Royal College of Art (1950–1953). At the RCA, Smith studied underJohn Minton, Ruskin Spear and Carel Weight.
During the 1950s, Smith's early work was in a neo-realist style known as "The Kitchen Sink School" featuring domestic subjects.
In the 1960s Smith abandoned realism and adopted a brightly coloured, abstract style comparable to those of Wassily Kandinsky and Piet Mondrian incorporating Constructivismand Biomorphism with elements of hieroglyphic and musical notation. Smith continued to develop and work in this style and did not return to realism.