"Ajax" was built at Vickers' shipyard, in Barrow-in-Furness, England. She was laid down on 7 February 1933, launched on 1 March 1934 and completed on 12 April 1935. She was commissioned for service on the North America and West Indies Station, but after working up in May 1935, she was deployed instead to the Mediterranean on detached service after the Abyssinian crisis. This lasted until November when she finally joined her squadron in Bermuda. Until 1937 she undertook exercises and visits to ports in the Americas. At the end of her West Indies deployment, "Ajax" returned to Britain for refit. At this time, her 4" battery was upgraded by exchanging single for double mountings.