Born in London, he spent much of his career with the Hudson's Bay Company in British Columbia on the west coast of Canada.
In 1844, he served as second mate of the Hudson's Bay Company steam bark Vancouver under the command of Captain Andrew Cook Mott.
He sailed to North America and arrived in Fort Vancouver, in what is now Washington state and then the "capital" of the Hudson's Bay Company's Columbia District, on 27 March 1845.
Scarborough then "declared him as a deserter and broke open his chest and proceeded to the extremity of the law… We shall be anxious to hear how it is settled as this officer is a favourite with us all".
Beaver had on board "a quantity of Indian trading goods not upon the manifest, to the value of $500; also that both vessels before reaching the port of entry, had anchored at Fort Nisqually for fifteen hours; that six passengers and their baggage had been landed without permit".
In 1854 the Mary Dare was due for renewal of her twelve-year registration and as no facilities existed for her inspection in British Columbia, William Mouat took her back to England.
Whilst in England, on 8 August 1854, he married Mary Ann Ainsley at St Dunstan's, Stepney, East London.
William Alexander and his new wife left England on 1 September 1854 and travelled back to Victoria as passengers on the Marquis of Bute.
Fellow passengers included the Reverend Edward Cridge, chaplain to the Hudson's Bay Company and his new wife also called Mary.
Edward Cridge became dean of the Anglican cathedral in Victoria, British Columbia, and later withdrew with about three hundred and fifty of his congregation (of whom William Mouat was one) and joined the Reformed Episcopal Church.
His findings were favorable and the Hudson's Bay Company built the steamship Marten at Savona's Ferry, British Columbia on the Thompson River at the west end of Kamloops Lake.
William Mouat, "one of the most careful and reliable men that ever handled a wheel", was given command of the Labouchere, which he took to San Francisco on 15 February 1866 to be fitted out for the accommodation of passengers.
William Mouat had displayed "admirable coolness, bravery and forethought" in saving his passengers but the official enquiry censured him for "very gross negligence…in not swinging the Labouchere to ascertain the deviation of the compasses before leaving San Francisco the steering apparatus having been shifted from aft forward" during the refit, and also for not having taken sufficient care of Her Majesty's mail.