Baxendale was educated at Preston Catholic College. After serving in the RAF, Baxendale took his first job as an artist for the local Lancashire Evening Post drawing adverts and cartoons. In 1952 he began freelance work for the children's comic The Beano, drawing series like Little Plum,Minnie the Minx (started in 1953, taken over by Jim Petrie in 1961), The Three Bears and The Bash Street Kids (initially called When the Bell Rings). He left The Beano in 1962.
Baxendale also co-operated on the launch of The Beezer in 1956 and Wham! (Odhams Press) in 1964. Baxendale worked for Fleetway (IPC Magazines), creating Clever Dick and Sweeny Toddler.
In the seventies Baxendale created the Willy the Kid series, published by Duckworths. In the 1980s he fought a seven-year legal battle with D.C. Thomson for the rights to his Beano creations, which was eventually settled out of court. In 1987 Leo Baxendale founded the publishing house, Reaper Books. In the same year he brought out THRRP!, an adult comic book. In 1990 he created I Love You Baby Basil! for The Guardian.