Born in Edinburgh, the son of a bookmaker, Neill attended Trinity Academy, and boxed out of the Sparta Amateur Boxing Club, representing Scotland at amateur level despite suffering serious injuries in a car crash.
He made his professional debut in May 1955 with a second round stoppage of Denny Dennis. He won his first 15 fights, including an eighth round stoppage of Matt Fulton in September 1956 to take the vacant BBBofC Scottish Area featherweight title, and a first round stoppage of Charlie Hill in December. He was named ‘Best Young Boxer of the Year’ in 1957 at the British Boxing Writers Awards. He suffered his first loss in January 1957, when he was stopped by the then unbeaten Jimmy Brown. His second defeat came three months later against Victor Pepeder. Later that year he was again seriously injured in a car crash, the resulting surgery shortening one of his legs, with surgeons telling him that he would never box again, but despite this Neill regained his fitness and continued to have success in the ring.
He challenged for Hill’s British featherweight title in April 1959 at Nottingham Ice Rink, stopping the defending champion in the ninth round after knocking him down nine times. Two months later he knocked out Terry Spinks in the ninth at the Empire Pool, Wembley. His next fight was a loss to Davey Moore, the American stopping him in the first round.
Neill started 1960 with wins over Alberto Serti, Germain Vivier, and Jimmy Carson, but was stopped in the fifth round in June by Johnny Kidd. In September he made the first defence of his British title against Spinks at the Royal Albert Hall. The fight was stopped in the seventh round due to cuts sustained by Neill. They met again for the title in November, Spinks this time knocking out Neill in the fourteenth round, leaving him in a coma and requiring surgery to remove a blood clot from his brain.