The Williams had been hatters for a number of generations,[3] dating back to an ancestor who settled in Ireland in the 1600s from Glamorganshire who was a felter.

[2] With the decline in his father's hatting business, Alexander and his brother Edward (1848-1905) started a sideline in taxidermy, founding Williams & Son, Dublin.

[2] Their father had learnt basic taxidermy from a Mr. Evatt of Mount Louise, County Monaghan, and he taught his sons.

[3] Both the hatters and the taxidermy shops co-existed at 1 Dame Street for a time and began what the ornithologist Richard M. Barrington described in the Irish Naturalist magazine as "the battle of the hats and birds", remarking that: In 1866, a fire broke out in the taxidermy workshop which destroyed the family business and killed six residents of the adjoining house.

Operating from 2 Dame Street, the business became a success from the 1870s, with private individuals and institutions such as the Natural History Museum, Dublin among their clients.

"[7] He remained largely self-taught, attending only the Royal Dublin Society night school for some lessons in drawing and painted in oils and watercolours.

[8] Following his election to the RHA as an associate member in 1884, he held his first solo exhibition at the Leinster Hall, Molesworth Street.

In 1899, Williams took a lease on a ruined cottage and three acres of land on the edge of Bleanaskill Bay, Achill Island.

He was commissioned by Blackie & Son in 1911 to produce paintings used to illustrate a set of four books entitled Beautiful Ireland.