Born in the Hulme area of Manchester, Williams spent some time as a pupil-teacher before following his father by becoming a musician, finding work as a clarinetist at the Comedy Theatre.
Concerned about working conditions in the industry, in 1893, he founded the Amalgamated Musicians' Union (AMU).
Shortly afterwards, Williams' mother, Kate, recruited a group of musicians in Birmingham and, within a year, branches had been set up in a large number of provincial cities.
[2] Williams' son, also Joe, served in World War I and was killed aged just eighteen.
[1] After many years of negotiations, in 1921, Williams persuaded the AMU's main rival, the National Orchestral Union of Professional Musicians, to merge into it.