The Great Northern class H4 was a 2-6-0 mixed-traffic locomotive designed by Sir Nigel Gresley. Its basis was the H3, but now it got three instead of two cylinders, being the first production locomotive to use Gresley's conjugated valve gear. All three cylinders worked on the second driving axle. With a huge boiler being six feet in diameter, the axle loading became somewhat high for some lines.

The first ten locomotives were built in 1920 at Doncaster and the LNER adopted this class as a standard design. With additional batches built at Doncaster, Darlington and three commercial manufacturers, 193 had been completed by 1937. They were designated class K3 by the LNER. Due to their rhythm of the exhaust beat and the uneven gyratory movements, they earned the nickname “Jazzers”.

Nevertheless, they were able to run at up to 75 mph (121 km/h) and were also used to haul express trains when needed. So they could be rated as being very successful, although Thompson rebuilt one in 1945 into the two-cylinder K5. All were withdrawn between 1959 and 1962 with none being preserved. The A1 steam trust once announced that they might build a new K3, but as of today no new news can be found about that topic.