Toynbee was part of a family multi-disciplined in the arts. He was the youngest son of Arnold Toynbee, historian and social philosopher; grandson of Gilbert Murray, classical scholar and poet; and great-grandson of George James Howard, Earl of Carlisle, the landscape painter. He is also the father of Polly Toynbee, journalist with the Guardian newspaper. Toynbee studied art at the Ruskin School of Drawing in Oxford and went on to teach art is a variety of colleges. As well as his paintings of the rail and underground stations, he is known for his depiction of sports and his ability to convey movement on the canvas.