Davidson went to Manchester Grammar School and then Oxford University where he obtained a degree in classics. He followed this with an MA at Columbia University in New York. He had hoped to take up dance choreography but realised that he would not be able to afford to do it properly.
He returned to Oxford University and continued with his work in classics at Wadham College. He took a scholarship at St Hugh's, and then became a junior research fellow at Trinity College.
In 1996 he was appointed to a lectureship at Warwick University. In 1999 he moved to Birkbeck College in London, where he became anniversary reader in ancient history.
His first book, Courtesans and Fishcakes: The Consuming Passions of
Classical Athens, is a re-write of his DPhil thesis.