Died 1809. He probably originated from Great Yarmouth, Norfolk, where families by the name of Cobb had long settled, and where he lived out the greater part of his life.
Cobb was commissioned lieutenant on 23 February 1774, in which capacity he commanded the small sloop Florida 6 on the Jamaican station for several years.
In the summer of 1779 he joined the cutter True Briton 10 for service in the Channel Islands, and he soon captured a French privateer, the crew of which he took into Portsmouth in July. He was promoted commander on 13 March 1782 and commissioned a captured American privateer as the Stormont 14, serving out of the Leeward Islands until the peace of 1783.
From 1787 he commanded the sloop Scout in the Downs and at the Nore, retaining her through the Spanish Armament of 1790. He was posted captain at the end of that crisis, along with many other officers, and with seniority from 21 September 1790 he left the Scout.
Cobb was at Yarmouth when the mutiny in the North Sea station broke out on 27 May 1797 and upon Captain Edmund Crawley vacating the command of the Lion 64 in apparent ill-health during the hours after the initial outbreak Cobb went aboard that vessel to take command with the acquiescence of the crew. The Lion later joined those ships that had mutinied at the Nore on 12 May, and Cobb was sent to the Admiralty with the mutineers’ demands in June, returning almost immediately to advise that nothing but their unconditional surrender would be sufficient to end the dispute. Once the fleets had returned to duty he sat on the court martial of several ringleaders.
He next commanded the Glatton 56 in succession to Captain Henry Trollope from August 1797, and after she was refitted at Yarmouth in the spring of 1799 he was present at the invasion of the Netherlands from August to October, being sent home in command of the squadron that escorted the captured Batavian fleet. Continuing to be based in the North Sea station, he commanded the Glatton under Vice-Admiral Archibald Dickson in the expedition to the Baltic from August to September 1800.
In November 1800 he removed from the Glatton to the veteran Prince of Orange 70, sailing from Sheerness for Yarmouth on the last day of the month and remaining with the North Sea fleet until the end of April 1802, when upon the peace the Prince of Orange went up the Thames to Chatham to be paid off.
Cobb appears to have retained a civil position with the navy for some time after the resumption of hostilities in 1803, for it was reported that he inspected the local Sea Fencibles at Yarmouth in the following year. He also wrote to the Admiralty complaining about the condition of several Dutch schuyts that had been purchased by the Treasury to be fitted out as gunboats for Commodore Sir Sidney Smith’s squadron off Flushing.
Cobb was advanced to flag rank on 28 April 1808. In November 1809 the newspapers reported that although he had been advanced to the rank of rear-admiral of the blue at the time of the King’s Jubilee on 25 October, he had in fact passed away two months previously, which indicated that his death had occurred in about August 1809. Probate occurred in April 1810.
The address in his will was given as Great Yarmouth where he had built a residence that was put up for sale shortly after his death.