Wonnacott trained at the Slade School of Fine Art from 1958–63. He then moved to Southend-on-Sea, Essex, where he still lives. His solo exhibitions include shows at the Scottish National Portrait Gallery in Edinburgh (1986) and the National Portrait Gallery in London (2000). He has also had artworks exhibited at the Barbican Centre, the Royal Academy, and the Tate Gallery, all in London.
In 1997, Wonnacott painted the British prime minister John Major. In 2000, he painted the British Royal Family in a 12-foot tall artwork.