Dodd was raised in Liverpool and attended Knotty Ash School. At the age of seven, Dodd was dared to ride a bicycle with his eyes shut. In doing so, he crashed and received facial injuries that resulted in his distinctive buck teeth. This feature would later become iconic in his performances.
Dodd's first big performance was at the Nottingham Empire and from then on he gradually rose to fame as he was viewed positively. In 1989, he was taken to court on charges of tax evasion. He reportedly had local school children perform in his acts and left them unpaid.
He was also found to have little money in his bank, instead having £36,000 in cash. When asked by the judge "What does a hundred thousand pounds in a suitcase feel like?", he famously replied "The notes are very light, M'Lord." He was later acquitted. The trial led to his use of the line "Let me introduce myself. I'm Kenneth Arthur Dodd, artists' model and failed accountant", while performing.