Reddall was commissioned lieutenant on 8 July 1762, and he was the first lieutenant of the Experiment 50, Captain Alexander Scott, at the unsuccessful attack on Charleston on 28 June 1776. His conduct on that occasion, when he fought the ship after his captain had lost an arm and the crew had suffered multiple casualties, resulted in Commodore Sir Peter Parker taking him aboard the pennant ship Bristol 50 as her second lieutenant.
In very short order he joined the Buckingham 70 which had been recommissioned as a storeship, and he was promoted commander on 23 August 1777, retaining the Buckingham as the storeship Grampus 30 until the autumn of 1778 and seeing service in North America.
Reddall was posted captain on 20 February 1779, and he commanded the Eagle 64 from the date of his post commission, going out to the East Indies with Rear-Admiral Sir Edward Hughes squadron in March of that year. He fought at the Battle of Sadras on 17 February 1782, where due to the method of the French attack his vessel was little engaged and saw no casualties, and he was subsequently at the Battles of Providien on 12 April where she was not in the thick of the action and casualties were twenty-two men wounded, Negapatam on 6 July where he lost four men killed and nine wounded and came under threat of capture towards the end of the engagement, and Trincomale on 3 September where casualties were eight men killed and fourteen wounded. He left the Eagle in the following year.
Reddall died at Taunton, Somerset, on 16 January 1791.
On 14 July 1784 he married Elizabeth Scott of Poole, Dorset.