Melvyn attended Barnsley College of Art in 1950 and went on to study at Manchester College of Art in 1955. He later studied further at Keele University, where he became interested in combined arts and education, researching an integrated curriculum. He lectured in art at the College of Education, Cheshire, Hackney College, London and the London Institute. He has also taught art and music across schools in London.
Robinson's first solo exhibition was in 1978 at the Acme Gallery, Covent Garden in London. He has since had solo exhibitions at the Cooper Art Gallery, Barnsley, The Air Gallery, London and The Gallery, Cadaques, Spain. He has had group exhibitions with the Whitechapel Community Arts across East London, where he was also involved in gallery education. More recently, he has had regular open studios at his Acme Studios in London, leading to a number of private commissions. In 2011, Robinson agreed to allow his daughter to represent him. 2012 marks the year his System of Painting is introduced to the public.