 He was the only son of John Archer, an Irish engineer from County Tipperary, and his wife Charlotte Lee, formerly of Kent, England.The first records show that Archer, at the age of 18, was taught under the guidance of Charles Beazley, an architect based in London.Commencing in April 1809, Archer remained under Beazley's instruction for the duration of his three-year term of articles before moving on to the office of John Rennie the Elder in April 1813 in the position of drawing clerk.