Maurice Denton Welch was born March 29, 1915, in Shanghai, to Arthur Joseph Welch, whose parents were English, and Rosalind Basset, whose family was originally from New Bedford, Massachusetts. Denton Welch was the youngest of four boys and spent his early childhood in Shanghai, with many visits to England.

In 1924, Welch was enrolled in a school in Kensington, and then in 1926-1929 he attended St. Michael's, a preparatory school in Uckfield, Sussex. While he was in school, his mother, with whom he was especially close, died in Shanghai during March of 1927; this event had a profound effect on her son. In 1929 Welch started attending school at Repton in Derbyshire. Welch started at the Goldsmith School of Art in New Cross in 1933, where he studied for three years; among his teachers was the printmaker and graphic designer Edward Bawden. At first he lived in a house where his brother Bill was also rooming, and then he moved into a house near Greenwich Park where the landlady was Evelyn Sinclair, who became a close lifelong friend.

On June 7, 1935, Welch was traveling by bicycle to go visit his aunt, when he was hit by a car. His spine was fractured, and for a few months he was paralyzed from the chest down. He was able to learn to walk again, but with difficulty. For the rest of his life he had kidney and bladder infections, which would cause frequent severe headaches. After the accident, Welch first spent time at National Hospital, and then in the Southcourt Nursing Home in Broadstairs, Kent. When he left the nursing home July 1936, Welch rented an apartment with Evelyn Sinclair in Tonbridge in order that he could be close to his doctor, John Easton. Sinclair remained with Welch as his housekeeper at his different residences until May 1946, two months after Welch and his partner Eric Oliver moved to Middle Orchard, the country house of Noël and Bernard Adeney at Crouch, near Borough Green, Kent. However, Sinclair returned to Middle Orchard in July 1948 to assist Welch until his death.

Welch continued to paint and draw after his accident. In 1941 the Leicester Galleries in London first exhibited some of his paintings, and continued over the next few years to include his paintings in their exhibits. The Leger Gallery and Redfern Gallery, both in London, also exhibited his works. Welch began writing in 1940, and some of his poems appeared in minor publications in 1941. In 1942, after the death of the painter Walter Sickert, Welch's article (an amusing account of his having tea with Sickert shortly before Welch left the nursing home in Broadstairs) was published by Cyril Connolly in the August . Welch received a letter of praise from Edith Sitwell. Soon after, Herbert Read, editor at Routledge, accepted Welch's manuscript for , and Dame Edith offered to write the foreword; she also wrote a review for the book. With her support, sold out before its May 1943 publication. The book received enthusiastic reviews, and Welch began writing , which was published in February 1945. He also wrote several short stories, and in the fall of 1945, as his health was worsening, Welch resumed his work on , a novel that he had begun earlier, and that was to remain unfinished at his death. Although Welch was to consider himself primarily a writer after the success of , he kept painting and drawing. Nine of his late paintings, created during a time when his health was failing, were reproduced in (published in 1951). He died December 30, 1948, at Middle Orchard Cottage in Crouch, Kent.