In 1974, at the age of 21, Conway was elected as a councillor of the Metropolitan Borough of Gateshead council. In 1977, he was also elected to the Tyne and Wear County Council, and was the Conservative group leader from 1979 until 1982. He stepped down from the county council in 1983, when he was elected to Westminster. At Gateshead he was the Deputy Conservative Group Leader for some years and remained a councillor at Gateshead until 1987, while simultaneously a Member of Parliament