Welch was born in Shanghai of Anglo-American parentage. He was sent to England to preparatory school and eventually Repton, where he was wretchedly unhappy. He ran away at 16, traveling to China once more, before returning to London and enrolling at the Goldsmith School of art.

He intended to be a painter, but he became an invalid for the rest of his life, after a devastating bicycle accident at age 20. His work include Maiden Voyage (1943), the novel In Youth Is Pleasure (1944), short stories in Brave and Cruel, and Other Stories (1949), and the autobiographical A Voice Through a Cloud (1950).