Barker was born in Waterford in 1773. He attended Trinity College Dublin and then Edinburgh medical school where he qualified as a physician. On qualification he returned to Waterford. Barker opened the first fever hospital in Waterford. After five years he went to Dublin and settled there. In 1804 he was appointed senior physician at Cork Street hospital. By 1808 he had become professor of chemistry at the University of Dublin. Barker established the first medical journal and edited the Dublin Pharmacopia, in 1826. He was Secretary to the Irish Board of Health between 1820 to 1852. Barker died in Dublin in 1859.