The company started in 1835 as James Kitson at the Airedale Foundry, off Pearson Street, Hunslet, with Charles Todd as a partner. Todd had been apprenticed to Matthew Murray at the Round Foundry in Holbeck, Leeds.
Initially, the firm made parts for other builders, until it was joined in 1838 by David Laird, a wealthy farmer who was looking for investments, and the company became Todd, Kitson and Laird. That year saw the production of the company's first complete locomotives, either for the North Midland or the Liverpool and Manchester Railway. However, Todd left almost immediately to form Shepherd and Todd, and the company was known variously as Kitson and Laird or Laird and Kitson.
The order for six engines by the Liverpool and Manchester began with 0-4-2 Lion,, which still exists. Around 1858, it was withdrawn from service and sold to the Mersey Docks and Harbour Board, where it was jacked-up off its wheels and used for pumping water. In 1930 it was restored and remains in preservation at the Museum of Liverpool.
In 1842, Laird, who not receiving the financial return he expected, left the partnership. Kitson was then joined by Isaac Thompson and William Hewitson, the company becoming Kitson Thompson and Hewitson. In 1851 the company exhibited an early tank locomotive at The Great Exhibition, and was awarded a gold medal. In 1858 Thompson left and the firm became Kitson and Hewitson, then, finally, Kitson and Company in 1863 when Hewitson died.
The company built about 5,400 locomotives over a period of 101 years, with orders for British railways, including the Midland Railway, the Lancashire and Yorkshire Railway and the South Eastern Railway, and worldwide. From 1855 many Indian railways became major customers.