When the South Eastern & Chatham needed new suburban tank locomotives for the south of London, Harry Wainwright used the existing 0-4-4T locomotives of the SECR's constituents as an inspiration. These were the SER's class Q and the LCDR's classes R and R1. To be specific, he used the R1 as basis for the development of the new class H.

Between 1904 and 1909, 64 were built by Ashford Works. After it was realized that actually two more had been ordered and only their parts manufactured, these two were completed in 1915. Most were used on ex-SER lines and only the 13 which were used on ex-LCDR lines had an additional Westinghouse brake. The boiler designed for the class H was later also used for rebuilding other classes.

All went to the Southern Railway and all but two were taken over by British Railways in 1948. In the following years, many of them were equipped for push-pull service and used on rural branch lines. Between 1952 and 1964, 64 were withdrawn. 31263, the last one to be withdrawn, was preserved and is owned by the Bluebell Railway since 2008, now in SECR livery and carrying the number 263.