Alan Summerley Cole was the son of Sir Henry Cole, K.C.B, a pioneer in design reform and the first director of the South Kensington Museum. In addition, F. S. Haden was a schoolmate of Alan Cole's uncle, Charles Cole, and he later became doctor to the Cole family. A. S. Cole married Margaret Elizabeth Clark in March 1879 and they had four children, Hilda (b. ca 1880, m. Jack Bennet), Muriel (b. ca 1882), Jack (b. ca 1884) and Doreen (1901-1903).
Cole attended the Government Design Schools at South Kensington, and later became the Assistant Secretary at the South Kensington Museum. He was an expert in textiles, especially lace, and was the author of a number of catalogues on the subject.
In 1849, when Whistler was living with the Hadens at Sloane Street, he met Cole and his elder sisters at a children's party given by the Dilkes. Cole and Whistler remained life-long friends and correspondents. In the spring of 1876 Whistler began a portrait of Cole's father which was taken up again in February 1882 but never finished as Henry Cole died on 18 April 1882. The picture appears to have been destroyed. Later in 1876 Whistler and Cole played together in Under the Umbrella, an amateur theatrical in Kensington Town Hall. In this year Whistler also gave Cole an number of spontaneous sketches he had made of The Blue Girl: Portrait of Connie Gilchrist (YMSM 207) and Arrangement in Brown and Black: Portrait of Miss Rosa Corder (YMSM 203). In 1879 Cole helped Whistler plan a trip to Venice.
Cole's diary records many dinners and breakfasts at Whistler's house during the 1870s in the company of such persons as Frank Dicey, Cyril Flower, Louis Huth, Richard Monckton Milnes, Oscar Wilde, Jacques Joseph Tissot, Frances Leyland, Janey Sevilla Campbell, George Adolphus Storey and Theodore Watts, when they had discussed such subjects as Japanese art, Velasquez, Balzac, Sarah Bernhardt and spiritualism. In his diary Cole also followed the progress of Whistler's decoration of the Peacock Room at Leyland's home in Prince's Gate in the autumn and winter of 1876, and made records of the exhibitions of Whistler's pictures, eg. Fine Art Society in 1881.
Cole, Alan S. (ed.), A Descriptive Catalogue of the Collection of Lace in the South Kensington Museum, London, 1881; Cole, Alan S., A Descriptive Catalogue of the Collection of Tapestry and Embroidery in the South Kensington Museum, London, 1888; Cole, Alan S., A Supplemental Descriptive Catalogue of Embroideries and Tapestry Woven Specimens Acquired by the South Kensington Museum Between 1890 and 1894, London, 1896; Cole, Alan S. and Henrietta (ed.), Fifty Years of Public Work of Sir Henry Cole, K.C.B., Accounted for in his Deeds and Writings, 2 vols, London, 1884; Bonython, Elizabeth, King Cole: A Picture Portrait of Sir Henry Cole, K.C.B., 1808-1882, London, n.d; Who was who: a companion to Who's who, London, vol. 3.