Sir Charles Dennistoun Burney was born in Bermuda on 28 December 1888, the only among the three children of Sir Cecil Burney, first baronet, and his wife Lucinda. Burney received a formal naval education, starting his training at the Britannia in 1903, and joining the battleship Exmouth as midshipman in early 1905. Burney joined the destroyer Afridi in 1909, and soon afterwards the Crusader, which used for experimental work by the anti-submarine committee, of which his father was the first president. Burney became very interested in the experiments then in progress for destroying submarines and was also quick to see the potential of the aeroplane as a means of spotting submarines, sparking off an interest in aeronautics.

When the First World War broke out, Burney was given command of the destroyer Velox, but soon afterwards he joined the Vernon, the Portsmouth torpedo school, where up to that time much of the navy's scientific research and development had taken place. At Vernon he was primarily responsible for the development of the explosive paravane, a small underwater aeroplane used to destroy submarines and mines. By 1916 he had taken out 11 patents dealing with paravanes and associated equipment and was rewarde dfor his work in the 1917 birthday honours by his appointment as CMG, an honour rarely given to a lieutenant. In 1920 Burney retired from the navy as a lieutenant-commander and at the age of 40 he was promoted on the retired list to commander. In 1921 he married Gladys, the younger daughter of George Henry High, of Chicago; they had a son. Burney succeeded his father in the baronetcy in 1929.

After the war, Burney took out a series of patents relating to precast concrete as a building material and joined Vickers Ltd as a consultant. He realized that the new developments in aviation held both economic and political implications. He set out hiw ideas were set out in a 1929 article entitled 'The World, the Air and the Future' and entered parliament as a Unionist member for Uxbridge in 1922, holding his seat until 1929. Burney was keen to start his airship service using the German Zeppelins surrendered to Britain at the cessation of hostilities, but these were found to be too corroded. After lengthy negotiations with Vickers and the government, Burney formed the Airship Guarantee Company, appointing Barnes Wallis as chief designer in 1923, and soon after Nevil Shute Norway, who became a novelist, as chief calculator. An order for a new airship, the R.100, was placed with Burney's firm, but the government decided that competition was healthy and put together its own design team at the Air Ministry (consisting mainly of members already discarded by Burney for his board on the advice of Barnes Wallis), to develop the R.101 at the Royal Airship Works at Cardington. This resulted in an unhealthy race between the two projects that eventually ended with the crashing of the R.101 on 5 October 1930 at Beauvais in France, killing forty-eight of the fifty-four people on board, including Lord Thomson, the secretary of state for air who had instituted this project, and the design team. This destroyed the British rigid airship programme for all time.

During the Second World War Burney was employed by the War Office on secret experimental work, the scope of which can be seen in a large number of patents that began to appear in the early 1950s relating to, among other matters, aerial gliding bombs and marine torpedoes with gyroscopically controlled aerofoils, gun-fired rocket projectiles, and a non-recoil gun. After the war, he became interested in improving fishing trawlers. He designed a catamaran trawler, apparatus to facilitate trawling and landing the catch, an otter or ‘porpoise’ (a kind of paravane) incorporating sonar to detect fish shoals, and plants for freezing fish either on board or ashore. In all, Burney took out more than one hundred patents during the period from 1915 to 1962. Among these were six with Barnes Wallis and one with Wallis and Nevil Shute Norway on aspects of airship design.

Burney died in Hamilton, Bermuda, on 11 November 1968.