Britain did continue developing tanks after World War I

Why did Britain fail to develop tanks further after World War I?

It did develop them; the interwar story is less famous, but Britain fielded a mechanized army and reliable, widely used tank designs.

Britain continued developing tanks throughout the 1920s and 1930s, although that work receives less attention than wartime designs. The army entered the war with extensively motorized logistics, subject to exceptions such as yeomanry units still being converted in the Middle East. Dunkirk's equipment losses did not mean a return to horse transport, while the Chindits' use of mules answered a particular jungle requirement. Matildas and Valentines were supplied widely, including to the Soviet Union, and their reliability receives particular praise. The Matilda's 40 mm two-pounder is described as a highly competitive anti-tank gun at the start of the war and through much of its early period.