Recent events demonstrate the need for greater understanding of intercultural relations between Muslim minorities and majority of cultures in host societies. We examine British Muslims' descriptions of their experiences of acculturation. Data from interviews with first‐generation Muslims were analysed by using discourse analysis. Participants' descriptions reflect the acculturation possibilities made available in local interactional contexts. Where invited to choose between assimilation and separation, participants provide ‘trouble‐telling’ accounts that detail the difficulties involved. In contexts involving integration, participants account for their own efforts. By contrast, contexts that allow participants to introduce acculturation in their own terms lead to descriptions of acculturation success. Thus, participants' accounts of relations with British culture reflect not simply orientations towards acculturation but rather how acculturation is framed and negotiated in local contexts: The success or failure of intercultural relations reflects as much how the issues are presented as they do immigrants' acceptance or non‐acceptance of British culture.