Painter and teacher, born in Sheffield. From 1943 to 1948 he was an apprentice signwriter, which he said taught him more than subsequent teaching. Won a Scholarship to Royal College of Art, 1948 -1952, followed by Abbey Major Scholarship to work in Italy, 1952-53, where he was influenced by the Italian Realists.
First solo exhibition held in London in 1953, when he was a notable member of the Kitchen Sink painters together with John Bratby and Edward Middleton. Together they exhibited at the Venice Biennale in 1956, in the following year appearing in the Looking at People show at South London Art Gallery and Pushkin Museum, Moscow.
Taught for several years at St Martin's School of Art. From the 1960s Greaves moved away from the Kitchen Sink subjects and his work became more poetic and linear. Graves Art Gallery in Sheffield held a retrospective of his work in 1980.
The Tate Gallery hold his work.