Leach first became involved in the comics industry in 1978, when he did one-off work for 2000 AD. He returned to work on their team The VCs, and soon became popular amongst fans. In 1981 he moved to Quality Communications, where he worked as art director and as the first artist on Alan Moore's Marvelman, and later worked with Moore on Warpsmith. He worked with Dave Elliott, where they used the pseudonym K. Edwards. In 1988 he and friend Dave Elliott set up their own publisher, Atomeka Press. Its major title was the anthology book A1, which won several awards. Both Atomeka and A1 ended in 1997. He continued to work on various projects during this time, collaborating with such artists and writers as Warren Ellis, Rufus Dayglo, and John McCrea in various roles. In 2004 Atomeka was briefly revived, but ceased publishing the following year. He has continued to work for various publishers in a variety of roles, including as artist, inker, writer, and editor. He has also published under the pseudonym Paul Behrer.
Leach was born and raised in the United Kingdom. In 1988 he won the Eagle Award for Favourite Single or Continued Story for his work on Marvelman. In 1999 he won the Eisner Award for Best Single Issue/Single Story for Hitman #34 "Of Thee I Sing".