Hedley Herbert Finlayson was born in Adelaide on 19 March 1895. His father, Ebenezer Finlayson, was born in 1848 and worked on paddle steamers on the River Murray for a number of years before becoming an Adelaide stockbroker and financial writer for The Register, Adelaide's largest newspaper at the time. He was also an early organiser for the newly formed Liberal Party. In 1884 Ebenezer married Finette (Nettie) Champion. She was said to be a pretty woman who became involved in local and church affairs.

Hedley Finlayson was the sixth of seven children, although two older sisters had died before he was born. He attended Kyre College in Mitcham (now Scotch College) for his early schooling.

In 1910 Finlayson enrolled with the Department of Chemistry at the University of Adelaide. During the course of his chemistry research in May 1913, Finlayson sustained permanent injuries in an accident. Finlayson seriuosly injured his right hand, head and face, and shattered his left hand when a device prematurely exploded whilst conducting tests with explosives at the Mitcham Quarry in South Australia. Doctors amputated his left hand and he lost the sight in his left eye. Finlayson’s father, Ebenezer, died five months later, in October.

In 1914 Finlayson was appointed junior demonstrator in the Chemistry Department at the University of Adelaide, where he remained until 1918. In 1917 he was also appointed to a committee investigating properties of the resin from the Yacca (Xanthorrhoea) tree. Germany had imported significant amounts of the resin before the outbreak of the First World War and it was thought it may be used in the manufacture of explosives. In 1918 Finlayson was awarded a Young Scholarship to conduct research into isolating and identifying the quinonoid colouring agents of Drosera Whittakeri, and into the constitution and properties of grass resin. Finlayson never graduated from his chemistry degree, although he became a Demonstrator in Chemistry in 1918 and was appointed Assistant Lecturer in 1921. His appointment as Assistant Lecturer was terminated in 1932 and in 1933 he was, once again, appointed as a Demonstrator. He worked in the Chemistry school of Adelaide University intermittently until 1958.

Possibly inspired by the work of Frederic Wood Jones (see AA 379), Finlayson developed a keen interest in the study of mammals in the early 1920s. He collected his first specimen in 1923 and became an Honorary Associate in Mammalia at the South Australian Museum in 1927, having already donated a number of skins. In 1927 he also published his first paper resulting from his studies. Finlayson went on to publish over sixty papers over the course of his career. In 1930 he was appointed Honorary Curator of Mammals at the South Australian Museum, a position he held until his retirement in 1965 at the age of 70. Upon his retirement from the museum the position of Curator of Mammals became a salaried one. Highly offended, Finlayson took most of his biological specimens with him when he left.

Finlayson travelled widely pursuing his interest in studying the mammal life of Australia. His expeditions were largely privately funded and were usually conducted in the summer months, during the break between academic years. In 1927 and 1928 he travelled to south-east South Australia and western Victoria seeking mammal specimens, particularly specimens of the larger wallabies in the area; the toolache, the brusher, and what was referred to locally as the ti tree wallaby. He then travelled to Melbourne and from there to Benalla near Mount Buffalo. In 1928 he spent three months in the Dawson Valley on the central Queensland coast studying a number of kangaroo and wallaby sub-species, as well as possums, koalas, gliders and bandicoots. In 1929 his pursuit of mammal specimens took him to the Flinders Ranges in South Australia. In 1929 and 1930 he visited islands in the Bass Strait as well as Waldheim in the Cradle Valley in Tasmania.

In September 1931 Finlayson received the skull and skin of a desert rat-kangaroo (Caloprymnus campestris) from Lou Reese of Appamunna Station in the Diamantina region of north-east South Australia. Caloprymnus campestris was thought to be extinct and no specimens had been found since 1843. In December 1931 Finlayson travelled to Clifton Hill Station in the Diamantina area and obtained a number of specimens. It was the last officially documented sighting of the desert rat-kangaroo and Finlayson’s rediscovery of it after nearly 90 years became one of his most notable professional achievements. He then travelled through the Basedow Range in the Northern Territory, and to Uluru and Mount Olga. In December 1932 he travelled again to Central Australia. Accompanied by Allan Brumby (see AA 42)Finlayson travelled through the Everard Ranges, Musgrave Ranges, Mann Ranges and the Tomkinson Ranges in north-west South Australia. In December 1933, accompanied by his brother Harvey in an automobile, Finlayson attempted to travel to the Rawlinson Ranges in Western Australia. In February 1934, having left his brother with the car which was found to be unsuitable, and having made his way towards the western end of the expedition route, he was abandoned by his travelling guides. He spent the next two and a half weeks making his own way back to Ernabella with two camels. In January 1935 Finlayson succeeded in his attempt to explore the Rawlinson Ranges but, again, his expedition was beset by disloyalty and conflict with people he had engaged to assist him. His travels in Central Australia during the early 1930s provided the material for his book, The Red Centre: Man and Beast in the Heart of Australia, 1935, Angus & Robertson, Sydney. Partly compiled from newspaper articles he published in Adelaide newspapers, The Advertiser and The Chronicle, during the early 1930s, The Red Centre was a great success and was reprinted eight times, the last time being in 1979.

Finlayson often relied on the assistance of Australian Aboriginal people to locate and obtain specimens on his expeditions.. He was among the first researchers to show museum specimens to Australian Aboriginal people to gain verbal information about the whereabouts, habits and range of mammals in the areas where he was working.

Finlayson did not return to Central Australia until the 1950s but he embarked upon numerous other expeditions. In 1947 he spent two weeks alone studying the fauna of Greenly Island off Eyre Peninsula in South Australia. In the 1950s he travelled to Central Australia and the Northern Territory. In roughly 40 years of travelling, Finlayson amassed a collection of approximately 3000 specimens and about 5000 photographic negatives.

Finlayson was awarded the Royal Society of South Australia’s Joseph Verco Medal in 1960 and in 1962 he was awarded the John Lewis Medal by the Royal Geographical Society of Australasia (South Australian Branch) Incorporated. After his death in August 1991, Finlayson was called a 'pioneer conservationist' in an obituary published in The Advertiser, an Adelaide newspaper, on 14 August 1991.

A significant collection of Finlayson’s personal papers, including a recipe book 1807-1827, reminisces of Finlayson and of Helen Finlayson 1878-1895, chemistry notes, papers relating to farming at Sheaoak Ridge, Kangarilla, field notes, specimen lists, bibliographies and correspondence 1921-1991, manuscripts of journal articles and of 'The Red Centre', personal diaries 1970-1991, Sir Joseph Verco medal and biographical notes are held in the State Library of South Australia (Ref: SL:M PRG 1092). His biological specimens were donated to the Strehlow Research Centre in Alice Springs.