Stokoe was born 1933 in London and studied at St Martin's School of Art 1953-57, going on to be a senior lecturer at Ravensbourne School of Art and Design for over 30 years. He also worked in marketing (Iliffe Press) and advertising.

Within the two phases of Stokoe’s career he has also branched out into other areas. For example, at times he has worked in mediums including hard-edge colour filled paintings and prints, Op-Art, wall based constructions and more latterly Fauvist-style works. He also produced three-dimensional works during a five-year period in the mid-1960s: ‘I was at the time emerging from a more gestural form of painting into experiments with the properties of pure colour, here exploiting gravity, height, perspective and balance’ (Letter to Paul Liss, 6 February 2007).

He was a member of the Printmakers' Council and showed at RA. He has had many one-man shows and his work is highly collected. His prints are held in collections such at the Government Art Collection and the V+A, and there are examples of his work in numerous public galleries, including those in Hull, Leeds, Liverpool and a large number of educational authorities.