Born in Adelaide, he was educated at Christian Brothers College and in 1896 became editor of the South Australian Catholic weekly The Southern Cross. A younger brother was Father Richard Denny, who in the 1930s was parish priest of Glenelg. Denny was elected to the Adelaide City Council in 1898 and in 1900 won the House of Assembly seat of West Adelaide, later renamed Adelaide. At the same time he studied law (though not at university) and in 1908 was admitted to the bar. Having joined the United Labor Party, he was attorney-general (with other portfolios) in the Verran government of 1910-12, the Gunn/Hill government of 1924-27 and the Hill government of 1930-33. Cabinets were small in this period, usually with only six members. As attorney-general, Denny undertook several reforms, including the 1911 Women Lawyers Act which enabled women to practise law. As minister for housing in the early 1920s, he was behind the Thousand Homes Scheme at Colonel Light Gardens. Denny served in Egypt and France during the First World War, was severely injured and was awarded the Military Cross. In 1920 he married Winefride Leahy. They had one son and three daughters.

The Great Depression was a testing time for governments everywhere. In 1931 the state ALP council expelled Premier Lionel Hill, his cabinet and other MPs for supporting the Premiers’ Plan, the fiscally conservative policy to cut wages and pensions and reduce expenditure. This was also opposed by the fiery New South Wales premier Jack Lang who formed his own Labor Party. The Hill government was heavily defeated in 1933 and Denny lost his seat of Adelaide to a Lang Labor candidate. He then left politics, practised law and wrote a book of essays on his war service and other subjects A Digger at Home and Abroad (1942). During the 1920s he moved from the city, and the cathedral parish, to Glenelg, and in his latter years he lived at Norwood. His state funeral was held at St Ignatius’, Norwood.