Cotes was born in London. At the age of fifteen he was apprenticed to George Knapton, a respected artist who had painted the royal family. Cotes was a founder member of both the Society of Artists and the Royal Academy. He was an important pastel portraitist as well as a skilled oil painter. Cotes was influenced by the continental pastellists, Rosalba Carriera and Maurice Quentin de la Tour. However, instead of the softly blended colours usually associated this medium, Cotes preferred bold tones.