Thomas Brownrigg was appointed assistant surgeon 21 March 1814 and appointed Staff Surgeon Royal Navy 17 July 1817
Thomas Brownrigg was Assistant of the Tonnant and served in her boats in the operations in the Chesapeake and coast of America including the capture of Washington and Baltimore, and served in the Cockchafer schooner of 4 guns, when she captured two privateers of superior force and a severe action with a slaver of 16 guns. 
He was appointed assistant surgeon to the Leander in 1819. 
Thomas Brownrigg was promoted to the position of Surgeon in the Royal Navy in 1824. Other men promoted at the same time included Joseph Steret and Andrew Douglas Wilson 
Medical and surgical journal of His Majesty's Hospital and Garrison at Ascension for 1 October 1837 to 19 January 1839 by Thomas Brownrigg - National Archives
He was employed as surgeon on the Tortoise to VDL in 1842. The Tortoise sailed from Plymouth 26 October 1841 and arrived in Van Diemen's Land on 19 February 1842 with 394 male convicts.
In the 1851 Census Thomas Brownrigg, aged 64 is recorded as a widower residing at Chatham. Occupation surgeon on half pay. He has one servant.
In the 1861 Census Thomas Brownrigg resided at Keighley as a lodger in the house of Michael and Elizabeth Craven. Age 74
Thomas Brownrigg died in 1866
This gentleman, who died at Keighley on the 18th inst. was an old surgeon in the Royal Navy, having joined the service nearly sixty years ago. He had been employed in various parts of the world, and in early life was at the capture of the City of Washington, acting with the naval force under Admiral Sir George Cockburn. He had served in the Baltic, North America, West Indies, East Indies, China, Australia, and the Pacific For several years he held an appointment as surgeon to the convict establishment at Bermuda (a naval depot and station in the Southern Atlantic); and it is believed the last public appointment he held was that of surgeon-superintendent of the *Dromedary convict ship when she took out 500 convicts to Tasmania. Of very retired habits, Mr. Brownrigg was but very little known in the vicinity where he spent the last few years of his life, but he was held in high esteem by his old naval friends and messmates, who had the opportunity of duly estimating his character and worth. Many of these friends have passed away, and all are hastening to that 'bourne from which no traveller returns,' but one of the number still living is thus permitted to give this little outline of the services of his friend and messmate, with whom he had been on terms of intimacy for a period of more than half a century. Mr. Brownrigg was a native of the county of Westmoreland.