[1][2][3][4] The young Campbell was educated at Ayr Academy, before going on to study at Glasgow University 1887–91 under noted classical scholars Richard Claverhouse Jebb and Gilbert Murray.
As a gifted student, he was awarded the Craven Fellowship in 1896 and went to continue his education in Greece at the British School at Athens, where he studied under Cecil Harcourt Smith.
Edgar took part in some important archaeological digs, including assisting David George Hogarth at the ancient city of Naukratis in 1903, and excavating the Tomb of Khesuwer at Kom el-Hisn in 1910.
He was buried in Rectory Lane Cemetery, the burial ground of the Church of St Peter, Great Berkhamsted and his grave is marked with a headstone carved in the shape of a papyrus scroll.
Edgar donated a number of his archaeological finds to the collection of the British Museum in London, including Cycladic and Minoan artefacts, and items from Naukratis.