Like most Bristol Engines designs, the Centaurus was based on the mechanicals of an earlier design. In this case the "classic" 5.75" piston from their original 1918 Jupiter was placed in a longer-stroke cylinder, which combined with the new cylinders made the displacement jump from the Hercules's 2364 cubic inches to a massive 3270, making it one of the largest piston aircraft engines built.
Scaling up smaller designs to the high-point of engine peformance is not an easy task. While Bristol maintained the engine dates to 1938, production couldn't start until 1942 (nor was there a need for it). In fact the engine didn't see any use until near the end of the war, first appearing on an upscaled version of the Vickers Wellington, the Warwick. Other wartime, or just-post-wartime, uses include the Bristol Brigand (and Buckmaster), Hawker Tempest and Fury, and the Blackburn Firebrand. The engine also saw post-war use in civilian airliners. It was used in the ill-fated Brabazon.
Other piston engines of this size were developed by both Pratt and Whitney and Wright, but neither could be considered as successful during the war. The Wright was famous for bursting into flame on takeoff, and both designs required considerable development periods before becoming reliable enough for civilian use. The Centaurus, on the other hand, was considered to be very reliable right from 1942, once the initial bugs had been worked out. The US engines saw greater numerical use however, a side effect of the sizes of the two aircraft industries in the post-war era.