Ashman's playing career was spent at Sheffield United, Nottingham Forest and Carlisle United. However, it is his managerial career that is more distinguished.
His managerial career began at Carlisle United, where he led them to the Third Division Championship and the following year to a third place in League Two.
In 1967 he signed for West Bromwich Albion, where he led them to glory in the 1968 FA Cup.
He then moved abroad to manage Olympiacos, before returning the UK with a managerial position at Carlisle United. In 1972/73 he led the club to the First Division.