Greenhalgh worked in the cotton industry from the age of 15 and joined the Bolton and District Card, Blowing and Ring Room Operatives' Provincial Association, becoming chair of his branch and also serving on the national executive of the Cardroom Amalgamation from the age of 24.
He soon moved to work full-time for the union, and at the age of 33, he became general secretary of the North East Lancashire Card and Blowing Room Operatives' and Ring Spinners' Association.
[1] In 1949, he was elected as general secretary of the International Federation of Textile Workers' Associations.
He negotiated a merger which, in 1960, formed the International Textile and Garment Workers' Federation, and remained general secretary of the new organisation.
He again became its first general secretary, but retired the following year, due to poor health.