Demotion beat me to it!
Yes he was told to use his natural voice. Do folks who only saw him in Inglorious Basterds not realize he doesn't really have an English accent? If you'd watched his films previously, this is just the way he talks. In Hunger he has a totally thick put on Northern Irish accent if anybody really wants to hear how Irish he can really sound. He has put on other accents and held them through an entire film, and in one interview, he jokingly put on a Connery sound that he was also told not to use. Really, I don't see how an accent could be so off putting in a film. McAvoy and Byrne aren't using their natural accents or previous incarnations' inflections, either.
All Roman Soldiers somehow have British accents, too, remember?