This report is predominantly concerned with the accommodation and more broadly the political negotiation of the difference represented by two British post-immigration communities, Black-Caribbeans and Asians, in particular British Muslims. Our concern with these two communities allows considering relevant debates about cultural diversity, claims for equality and accommodation and the political response to such claims. In fact, most of the currently salient issues and conflicts over equality and cultural diversity can only be understood in the historical context of how these communities have made themselves heard and of how their claims and politics have been perceived as a ‘challenge’. The mobilization for religious equality and for the public accommodation of religion occurs against the background of concerns that have been raised and debated since, and even before, the Rushdie Affair of 1989/90. Contemporary struggles for racial equality are connected to the historical experiences of Black Caribbeans and to the mobilization and protest in response to inequality and discrimination, such as the Brixton uprising of 1981. While we do not wish to marginalize experiences and issues that do not fit these two narratives, we believe that a discussion of the most salient ‘diversity challenges’ of contemporary Britain needs to begin with these accounts.