Edward Thompson was born in Jamaica in 1840. His father was Edward Thompson, the Custos of Clarendon and member of the Assembly for the same parish; his mother was Eliza Hayhurst Poole, daughter of Samuel Poole, of Ludlow Estate, Clarendon. His wife, Georgiana Susanna McKenzie, whom he married in 1864, was from an old Scots-Jamaican family; her earliest Jamaican ancestor was Sir Alexander McKenzie, who had settled in Jamaica after being involved in an expedition to Darien, presumably the ill-fated one in the late 1690s. His younger brother was later the owner of the Seville Estate, near St Ann's Bay.
In 1842 the very young Edward travelled to England with his mother and aunt, and the family settled in Cheltenham, where he received his early education. Later he went to Rugby, the ‘public school’ reformed by Dr Arnold in the 1830s, and in 1859 to University College, Oxford. However he had to leave Oxford after only one year, because of his father’s money problems.
He apparently returned to Jamaica briefly, but in 1861 applied for a post as an assistant at the British Museum, which he obtained. He worked at first in the principal librarian's office, but was soon moved to the Department of Manuscripts. In 1867 he qualified as a barrister, but never practised. In 1866 he had been made assistant to the Keeper of the Manuscripts, and in 1871 he was made Assistant Keeper of the Manuscripts. He had now firmly embarked on a career which was to have enormous significance for the development of the British Museum far into the future.