I can assure you that this issue is not specific to immigrants or immigrant communities. The problem is much more general. Multiculturalism, I believe, is a good thing but there also needs to be a positive common culture. Unfortunately there isn't one to speak of. Britain is full of parallel societies and recently the main divide, that is being that is being highlighted recently, is the divide between normal citizens and those that happily and deliberately choose themselves above others. This is merely a dramatic and serious symptom of a problem that has been growing for some time.
Well if anything, immigrants, who choose to move their whole lives to Britain, should love Britain and its traditions even more than random British folks who happen to be born there.
Being brought up in a certain culture is a pretty powerful influence on who you are and what you like.
And people who choose to immigrate to a country may do so for a variety of reasons; I know a number of anglophones who hate living in Germany and are only here because of work.
I don't think that's true at all. I suspect the vast majority of people emigrate for economic reasons, not because they like another country's traditions.