Fourth son of Christopher and Anne Michell. He first went to sea at about eight years of age in 1718.
He was promoted to be lieutenant of the Advice with Captain William Martin on 11 Apr 1729. He afterwards served in the Royal Oak and Ipswich, and in August 1738 was promoted to the command of the Terrible Bomb, employed in the North Sea.
In 1740 he commanded the Swift sloop in the Channel; and in June 1740 was posted to the Pearl frigate, one of the squadron which, on 18 Sept 1740 sailed for the South Seas under the command of Commodore George (afterwards Lord) Anson. At Madeira he was moved into the Gloucester of 50 guns, the only ship of the force, besides the Centurion, which doubled Cape Horn and reached Juan Fernandez. The suffering of her crew from scurvy and want of water had been very great, and many men had died. When the few survivors had recovered their health, and with such reinforcements as circumstances permitted, the Gloucester rejoined the Commodore off Paita in November 1741, continued with him during the remainder of his cruise on the American coast, and sailed with him for China. The sickness broke out again worse than before, and in a violent storm the ship lost her topmasts and sprung a leak. With jury-topmasts she sailed so badly as to endanger the safety of her consort; she had only sixteen men and eleven boys able, in any way, to do duty, and many of these were sick. She had seven feet of water in the hold and there was no means of freeing her or of stopping the leak. It was therefore determined to abandon her and set her on fire. Michell with the miserable remnants of his ships company went on in the Centurion to Macao whence he took passage home in a Swedish ship. He arrived in England in 1743, and in October was appointed to the Worcester in which he joined the fleet under Sir John Norris in January 1743-4.
He was afterwards Commodore of a small squadron on the coast of Flanders and off Dunkirk, on which service he continued until March 1748, when on the plea that his private affairs required his presence in England, he was permitted to resign his command.
In 1747 he was elected Member of Parliament for Westbury; his elder brother dying that same year.
He married in 1749 Frances, daughter of Mr Ashfordby of Norfolk Street, London, with whom, it was announced, he received a fortune of £20,000.
He himself died "in the prime of life", 29 April 1752, and his remains were deposited in the Michell family vault in All Saints Church, Chitterne. (Now located in All saints graveyard.) There is a mural monument to him in the present church.