William was the second son and one of eleven children of Samuel Priestman, who had moved to Hull after retiring as a corn miller in Kirkstall, Leeds, and who in retirement had become a director of the North Eastern Railway Company. The family were strict Quakers, so William was sent to the Quaker School in Bootham, York. He left school at the age of 17 to start an engineering apprenticeship at the Humber Iron Works, but this company failed so the apprenticeship was continued with the North Eastern Railway, Gateshead. In 1869 he joined the hydraulics department of Sir William Armstrong & Company, Newcastle upon Tyne, but after a year there his father financed him in business at a small, run down works, the Holderness Foundry, Hull. He was soon joined by his brother, Samuel, their main business being the manufacture of dredging equipment (grabs), cranes and winches. In the late 1870s William became interested in internal combustion engines. He took a sublicence to manufacture petrol engines to the patents of Eugène Etève of Paris from the British licensees, Moll and Dando. These engines operated in a similar manner to the non-compression gas engines of Lenoir. Failure to make the two-stroke version of this engine work satisfactorily forced him to pay royalties to Crossley Bros, the British licensees of the Otto four-stroke patents.
Fear of the dangers of petrol as a fuel, reflected by the associated very high insurance premiums, led William to experiment with the use of lamp oil as an engine fuel. His first of many patents was for a vaporizer. This was in 1885, well before Ackroyd Stuart. What distinguished the Priestman engine was the provision of an air pump which pressurized the fuel tank, outlets at the top and bottom of which led to a fuel atomizer injecting continuously into a vaporizing chamber heated by the exhaust gases. A spring-loaded inlet valve connected the chamber to the atmosphere, with the inlet valve proper between the chamber and the working cylinder being camoperated. A plug valve in the fuel line and a butterfly valve at the inlet to the chamber were operated, via a linkage, by the speed governor; this is believed to be the first use of this method of control. It was found that vaporization was only partly achieved, the higher fractions of the fuel condensing on the cylinder walls. A virtue was made of this as it provided vital lubrication. A starting system had to be provided, this comprising a lamp for preheating the vaporizing chamber and a hand pump for pressurizing the fuel tank.
Engines of 2–10 hp (1.5–7.5 kW) were exhibited to the press in 1886; of these, a vertical engine was installed in a tram car and one of the horizontals in a motor dray. In 1888, engines were shown publicly at the Royal Agricultural Show, while in 1890 two-cylinder vertical marine engines were introduced in sizes from 2 to 10 hp (1.5–7.5 kW), and later double-acting ones up to some 60 hp (45 kW). First, clutch and gearbox reversing was used, but reversing propellers were fitted later (Priestman patent of 1892). In the same year a factory was established in Philadelphia, USA, where engines in the range 5–20 hp (3.7–15 kW) were made. Construction was radically different from that of the previous ones, the bosses of the twin flywheels acting as crank discs with the main bearings on the outside.
On independent test in 1892, a Priestman engine achieved a full-load brake thermal efficiency of some 14 per cent, a very creditable figure for a compression ratio limited to under 3:1 by detonation problems. However, efficiency at low loads fell off seriously owing to the throttle governing, and the engines were heavy, complex and expensive compared with the competition.
Decline in sales of dredging equipment and bad debts forced the firm into insolvency in 1895 and receivers took over. A new company was formed, the brothers being excluded. However, they were able to attend board meetings, but to exert no influence. Engine activities ceased in about 1904 after over 1,000 engines had been made. It is probable that the Quaker ethics of the brothers were out of place in a business that was becoming increasingly cut-throat. William spent the rest of his long life serving others.