Barker's relationship to painting is most clearly expressed in the 'homage' series of works. By transforming flat images into insistently physical, three-dimensional objects, he created sculptures that can best be understood as monuments to painting and as celebrations of their timelessness and quality of invention. As a young artist, Barker had met René Magritte (1898-1967) in 1964 at the Hanover Gallery in London and expressed his admiration for the Belgian Surrealist following his death in 1967 with the works Magritte's Pipe and Madame Magritte's Pipe, which feature two iconic themes of the Surrealist painter's subject matter.

Barker's works are in a number of collections including the British Museum, London; Imperial War Museum, London; Museum für Moderne Kunst, Frankfurt; The Hirshhorn Museum & Sculpture Garden, Smithsonian Institution, Washington D.C.; Museum of Modern Art, Lisbon; Städtische Kunsthalle, Mannheim; Tate Modern, London; Victoria and Albert Museum, London; Collection of Sir Paul McCartney; Collection of Jude Law.