Born in Newport, in Wales, Twomey worked as a labourer, and was an early member of the National Amalgamated Labourers' Union (NALU); by 1891, he was a member of the union's executive committee.
[3] Twomey was a supporter of the Labour Party, and, after several attempts, was elected in 1904 to represent the Central ward on Newport Council.
[5] Twomey was a strong supporter of adult education and, under his leadership, NALU instituted a scholarship to Ruskin College.
He took part in union merger discussions which, in 1921, led NALU to become part of the Transport and General Workers' Union, and he served as its national organiser for general workers.
In 1946, Twomey deposited his papers, which included many records of NALU, with the National Library of Wales.