Samuel Henry Drew was born in Maidenhead, Berkshire, England, on 17 November 1844, the son of Fanny Booker and her husband, Henry Drew, a watchmaker and jeweller. Soon after Samuel's birth the family moved to Ventnor on the Isle of Wight. In the early 1850s they emigrated to Van Diemen's Land (Tasmania), where Drew was educated at the Launceston Grammar School. After completing his education he was sent to London to serve his apprenticeship to the watchmaking trade.
After Samuel's return to Tasmania, the family emigrated to Nelson, New Zealand, where they arrived on board the Lallah Rookh on 12 August 1860. Henry Drew practised his trade in Trafalgar Street, and it is likely that his son worked with him until August 1870 when Samuel moved to Wanganui. There he entered into business on Taupo Quay, where he established his jewellery and watchmaking business.
Drew returned to Nelson in 1872, and on 8 May married Catherine Alice Beatson, daughter of William Beatson, a well-known architect. They established their home in Wanganui, where they raised a family of four boys and four girls. Another daughter died in infancy.
Drew became successful in his profession, but was better known for his interest in natural history and geology. His family helped to collect and classify his specimens of molluscs, birds, beetles and other fauna, as well as Maori artefacts. His activities extended as far as Kapiti Island, where he became something of an authority on the local birds and fish. Drew supplied specimens to collections throughout New Zealand. He exchanged specimens with Julius von Haast, and on two visits in 1886 and 1888 Andreas Reischek helped to classify his collections. Reischek also trained Drew's son Henry as a taxidermist. Drew published several articles on natural history in the Transactions of the New Zealand Institute, and was made a fellow of the Linnean Society of London in 1897.
As the fame of Drew's collections grew, an increasing number of visitors were drawn to what, since 1880, had become an extensive museum established in the family home. By 1890 the problem of space – both for the collections and Drew's family – had become so acute that Drew proposed selling the collection on condition that it become the nucleus of a public museum. It was valued by Sir James Hector at £1,186 12s., but Drew sold it for about half this amount. Prisoners from the local gaol were used to prepare the site for the museum building at Queens Park. Drew acted as honorary curator, and the task of transferring and arranging the collection occupied six months. The Wanganui Public Museum was opened on 24 March 1895.
Full with future plans and busy in his work, Samuel Henry Drew died from a sudden heart attack at his shop on 18 December 1901; Catherine Drew died in 1925. Drew had made a significant contribution to the life of Wanganui. He was a member of the Harmonic Society and president of the Wanganui Orchestral Club, and also belonged to the Wanganui Rowing Club. He was known as a ready conversationalist, and a man of determined character with 'a genial and humorous temperament.' He is commemorated in a marble bust and memorial tablet in the Wanganui Regional Museum.