William Leyson was appointed to the position of Assistant Surgeon on 4 August 1810.
He was educated at St George's Hospital, where he was entered as a six-months' surgical pupil to John Griffiths in 1810. In August, 1815 he took out a further course of six months. 
He was included on a list of Certified Apothecaries in 1816 .
In 1824, still an assistant-surgeon, William Leyson joined the Expedition of Captain George Francis Lyon on the Griper to the Arctic. .......Captain Parry's history of the expedition is well known; in the preface to which he declared his happiness “ thus publicly to express the high sense I entertain of the laudable zeal and strenuous exertions uniformly displayed by Captain Lyon,” as well as by all his other comrades.
Capt. Lyon’s “Private Journal” was also published, and has been aptly termed “The Sayings and Doings of the Esquimaux.” He was rewarded with post rank dated Nov. 18. 1823; and on the 16th of January he was presented with the freedom of his native city of Chichester, and entertained by the Corporation at a public dinner. The freedom was enclosed in an oaken box, turned from a portion of the Hecla, lined with gold, and bearing the following inscription :-‘‘ Presented, Jan. 16. 1824, by the Mayor, Aldermen, and Citizens of Chichester, to George Francis Lyon, Esq., Captain in the Royal Navy, in testimony of their admiration of the zeal, perseverance, and spirit of enterprise displayed by him in his travels in Northern Africa, and in the late voyage to the Polar Sea, in search of a north-west passage.”
A few days before this gratifying occurrence, Capt. Lyon had been appointed to the Griper bark, fitting out for another voyage of discovery in the icy regions. This vessel was originally a gun-brig of only 180 tons burthen; but she had been considerably strengthened and raised upon, to enable her to accompany Lieut. Parry in the expedition of 1819; and her complement now consisted of forty-one persons, including Captain Lyon; Lieutenants Peter Smith Manico and Francis Harding; Mr. Edward Nicholas Kendall, assistant-surveyor; Mr. John Tom, midshipman; Mr. Thomas Evans, purser; Mr. William Leyson, assistant-surgeon, and three warrant officers.
She sailed from the Nore on the 16th of June, 1824, for the purpose of making an attempt to connect the western shore of Melville Peninsula with the important discoveries of Captain Franklin; and was accompanied as far as the coast of Labrador by the Snap surveying-vessel, which had been ordered to carry out a spare bower-anchor and part of her stores. When these were all on board, her decks, chains, and launch were completely filled with casks, spars, plank, cordage, etc and her draft of water was upwards of 16 feet aft and 15 feet 10 inches forward. “Had I succeeded in reaching Repulse Bay,” says her captain, “with less stores than I now carried, certain starvation would have attended us all, if we were detained, as might have happened, a second winter. To give some idea of the weather,” in which they were removed from the Snap, “it will be sufficient to say, that, during the whole of the time we were at work, the vessels were so entirely hidden from each other, by a dense fog. 
William Leyson was appointed to the position of Surgeon on 21 February 1825
He was employed as Surgeon on the Impregnable in 1842
He was employed as Surgeon Superintendent on the convict ship Henry Wellesley to New South Wales in 1837. He kept a Medical Journal from 2 June 1837 to 3rd January 1838.
He is entered in the British Medical Directory of 1853 -
Leyson, Wm. Neath, Glamorganshire -
F.R.C.S. (Nom) 1844;
M.R.C.S.E. and L.S.A. 1816.
William Leyson died on 3rd November 1854 at Neath in his 64th year.