Briggs was born in Wimbledon, London, England, to parents Ethel and Ernest Briggs, a lady's maid and a milkman. He attended Rutlish School for Boys (then a grammar school), pursued cartooning from an early age and, despite his father's attempts to discourage him from this unprofitable pursuit, attended the Wimbledon School of Art to study painting, and Central School of Art to study typography. He was conscripted into the Royal Corps of Signals at Catterick where he was made a draughtsman. After 2 years of National Service, he returned to the study of painting at Slade School of Fine Art, graduating in 1957. After briefly pursuing painting, he became a professional illustrator and soon began working in children's books. In 1961 he began teaching illustration at Brighton School of Art, which he continued until 1986.

In 1958, he illustrated Cornish Folk and Fairy Tales, a fairy tale anthology by Ruth Manning-Sanders that was published by Oxford University Press.

His first three major works, Father Christmas, Father Christmas Goes on Holiday (both featuring a curmudgeonly Father Christmas who complains incessantly about the "blooming snow"), and Fungus the Bogeyman, were in the form of comics rather than the typical children's-book format of separate text and illustrations. The Snowman (1978) was entirely wordless, and illustrated with only pencil crayons. Briggs said that it was partly inspired by his previous book, "For two years I worked on Fungus, buried amongst muck, slime and words, so... I wanted to do something which was clean, pleasant, fresh and wordless and quick." The Snowman became Briggs' best-known work when in 1982 it was made into an Oscar nominated animated cartoon, that has been shown every year since on British television.

Briggs continued to work in a similar format, but with more adult content, in Gentleman Jim (1980), a sombre look at the working class trials of Jim and Hilda Bloggs, closely based on his parents. When the Wind Blows (1982) confronted the trusting, optimistic Bloggs couple with the horror of nuclear war, and was praised in the British House of Commons for its timeliness and originality. The topic was inspired after Briggs watched a Panorama documentary on nuclear contingency planning, and the dense format of the page was inspired by a Swiss publisher's miniature version of Father Christmas. This book was turned into a two-handed radio play with Peter Sallis in the male lead role, and subsequently an animated film, featuring John Mills and Peggy Ashcroft. The Tin-Pot Foreign General and the Old Iron Woman (1984) was a scathing denunciation of the Falklands War. However, Briggs continued to produce humour for children, in works such as the Unlucky Wally series and The Bear.

He was recognized as The Children's Author of the Year in 1993 by the British Book Awards.His graphic novel Ethel and Ernest, which portrayed his parents' 41-year marriage, won Best Illustrated Book in the 1999 British Book Awards.

His wife Jean, who suffered from schizophrenia, died from leukaemia in 1973, only two years after his parents. They did not have any children.

As of 2008, he lives in Sussex in a small house; due to the clutter, he keeps a separate home from his partner Liz, her children and grandchildren. He continues to work on writing and illustrating books.

• The Snowman (1982) VHS ISBN 0-7912-0007-8

(1982) Sony Video Software: 50QS 4011(Betamax)/50ZS 4011(VHS)

(2006) DVD NR, UPC 043396164369, Director Diane Jackson, approx. 29 minutes

• When the Wind Blows (play) (1983) Little Theatre, Bristol and Whitehall Theatre, London.
• When the Wind Blows (1986)
• Father Christmas (1991)
• 1998 DVD NTSC fullscreen ISBN 0-7678-2670-1 UPC 4339603227 combines:

The Snowman (1993) 29 min; and

Father Christmas (1997) 25 min (including material from Father Christmas Goes on Holiday)

• The Bear
• Ivor the Invisible (2001)
• Fungus the Bogeyman (2004)
• Ethel and Ernest (2008) (still in production)
• Gentleman Jim BBC Radio 4 Afternoon Play, 4 May 2008

Briggs has won numerous awards during his career, including:

• 1966 Kate Greenaway Medal, for The Mother Goose Treasury
• 1973 Kate Greenaway Medal, for Father Christmas
• 1977 Francis Williams Award for Illustration (Victoria and Albert Museum), for Father Christmas
• 1979 Boston Globe-Horn Book Award
• 1979 Silver Pen Award, in Holland
• 1982 Children's Rights Workshop Other Award
• 1982 Francis Williams Award for Illustration (Victoria and Albert Museum), for The Snowman
• 1992 Kurt Maschler Award, for The Man
• 1992 Children’s Author of the Year, British Book Awards
• 1998 Illustrated Book of the Year, British Book Awards, for Ethel and Ernest
• 2001 Nestlé Smarties Book Prize Silver Award, for Ug