|Sir W G Armstrong Whitworth & Co Ltd
In 1847, the engineer William George Armstrong founded the Elswick works at Newcastle, to produce hydraulic machinery, cranes and bridges, soon to be followed by artillery, notably the Armstrong breech-loading gun, with which the British Army was re-equipped after the Crimean War. In 1882, it merged with the shipbuilding firm of Charles Mitchell to form Armstrong Mitchell & Company and at the time its works extended for over a mile (about 2 km) along the bank of the River Tyne. Armstrong Mitchell merged again with the engineering firm of Joseph Whitworth in 1897. The company expanded into the manufacture of cars and trucks in 1902, and created an "aerial department" in 1913, which became the Armstrong Whitworth Aircraft subsidiary in 1920.
Note - there might be a few builders in this list that are not in Leeds as they built Leeds designed locos as sub contractors.