After playing for local youth club Cromwell, Aizlewood joined his home-town club Newport County at the age of 14, turning down an offer to join Arsenal. Earning a wage of five pounds per week to cover expenses, he made his professional debut two years later at the age of just 16, whilst he was still attending school. He played for Newport for three years, leaving in 1978 to join Luton Town for a fee of £50,000, becoming David Pleat's first signing at the club. After four seasons at Luton, winning the Second Division title in his final year, he moved on to Charlton Athletic in 1982, again for a fee of £50,000. He was later appointed club captain and was named the club's player of the year for both the 1984–85 and 1985–86 seasons.