Alcock attended Trinity College Dublin (TCD), graduating with a BA in natural sciences in 1893, and MB, BCh, BAO and MD in June 1896.

[4] Alcock went on to teach anatomy in Victoria College, Manchester, and physiology at TCD.

In 1902 he was appointed a research fellow at the University of Marburg working with Professor Hans Horst Meyer.

In January 1903, he was appointed a physiology demonstrator at the new department at the University of London under Augustus Desire Waller.

Alcock took up a position as lecturer on physiology in January 1904 at St Mary's Hospital Medical School, becoming vice-dean in 1906.