Born in Hulme in Manchester as Sarah Welsh, Dickenson left school at the age of eleven to work in a cotton mill, where she became interested in trade unionism.
In 1895, she was appointed as joint organizing secretary of the new Manchester and Salford Women's Trade Union Council (WTUC).
[1] By 1905, Dickenson was frustrated with the NESWS's preference to engage with middle-class groups, rather than the labour movement, and she resigned along with Christabel Pankhurst and several other leading members, instead forming the National Industrial and Professional Women's Suffrage Society.
[1] Dickenson worked with Mary Macarthur to organise a National Union of Women Workers conference in Manchester in 1907.
[1] Dickenson opposed World War I, and was a delegate to the Women's International Conference on Peace at The Hague, although she was unable to travel to it, due to wartime restrictions.