Born in Ipswich, Suffolk, Donowa began his career with Norwich City. He was a member of the Norwich youth team that won the FA Youth Cup in 1983 and the side that won the League Cup in 1985. He was capped by England under-21s during his time at Carrow Road. In 1985–86 Donowa spent time out on loan at Stoke City where he played five times scoring once which came in a 3–2 win away at Millwall. In March 1986 he signed for Spanish club Deportivo de La Coruña for a fee of £50,000. After four years at the Estadio Riazor he played for a short time at Dutch side Willem II.