The Battle of Britain was a notable phase of the Second World War, an aerial conflict taking place between 1940 and 1941. Its intent by Nazi-controlled Germany was to gain air supremacy in United Kingdom airspace, prior to an invasion.
The Battle of Britain was one of Julian Bashir and Miles O'Brien's favourite holoprograms at Quark's holosuites, taking the role of two RAF pilots in a squadron that included Clive. The pair were intent on recreating the historical setting exactly, and had their own costumes. O'Brien even abandoned his Irish accent for his role.
Following the bombing of the Antwerp Conference in 2372, the two had an appointment to run the program. However, after part of their session, they felt their heart wasn't in it, and chose not to restart the program. They attempted to invite Odo to join the simulation, but the Changeling was enroute to Earth and had to decline. (DS9: "Homefront")
The two often let the program play out for several hours - something which proved costly when Keiko O'Brien returned from Bajor, and the two had to rush to clean O'Brien's quarters before she arrived. (DS9: "Accession")
When the crew returned to Deep Space Nine following Operation Return in 2374, O'Brien and Bashir's first action was to determine if the holosuites were working, and book a session in the program. ("Sacrifice of Angels")