Addington was a woolen merchant. At the time of the 1871 census he was a widower living at 105 and 106 St Martin's Lane, London.
He was a major collector, a member of The Arts Club (of which Whistler was also occasionally a member), and a member of the Burlington Fine Arts Club, from which Whistler resigned in 1867.
Addington's porcelain was sold at Christie's, London, on 8 March 1865, his copy of Turner's Liber Studiorum on 26 April 1883, his paintings and modern watercolours at Christie's, London, on 22 May 1886 and his Old Master prints, at Sotheby's, 27 May-5 June 1886.
UK census 1871; auction catalogues (listed above).