Quinn was born in Liverpool, and studied at the Ruskin School of Drawing, Oxford, and the Slade School of Fine Art. In 2003-4 he was chosen to be Artist in Residence at Tate St Ives, and in 2004 he exhibited solo at the Tate St Ives with the title 'Utopia Dystopia'. In 2007 another solo exhibition at the Wilkinson Gallery, London was entitled 'My Great Unhappiness Gives me a Right to your Benevolence'. Also in 2007 he was selected for the survey show at the Tate St Ives, entitled Art Now Cornwall, and one of his exhibits was Asleep by the Light of Glowworms (2005).

In 2010 he was appointed to the panel of judges for Britain's largest contemporary painting competition, the John Moore's Painting Prize.