I think in many parts thats an over played narrative based on extremism in religious views rather than cultural views, which happens in all religions BTW.
I grew up in a massively multicultural upbringing amongst Turkish, West Indian, Bangla, Pakistani and as a community it worked well, loads of community activities, loads of integration, many of those people although loyal to their roots seeing themselves as British.
People often don't want to accept that in many places multiculturalism has been a success, but it has and its evident in food, music, art, sport and in many communities around the country