The majority of shows blow off language barriers if it makes storytelling inconvenient. Sunrise isn't particularly unique in doing this.
If they wanted to be hardcore about it, the Britannians would speak English, the Elevens would have been forced to learn it after the occupation and use it in public, but would still speak Japanese to each other in private. Lelouch would speak Japanese as Zero (except for his public appearances) as an additional measure to conceal his voice. But that's not practical, especially for a Japanese-made show, though I suppose you could deal with the language barrier in the weird way that Black Lagoon dealt with it in the Japan arc.
I always thought it would have been cool if the English dub had the Britannians speak in British accents and the Japanese speak in American accents (and Lelouch uses an American accent as Zero and a British as Lelouch, same with Kallen in student/rebel modes.)