Whether or not one supports the principle of multiculturalism depends on how one defines it.
If it is tantamount to the doctrine of "separate but equal" espoused by segregationists in America, then it is doomed. If it means lumping people together in monolithic cultural categories which are seen as fixed identities, then it is doomed.
However, I do not believe that multiculturalism should mean either of these things. It should mean an awareness that we all have multiple identities and allegiances, which vary according to context. I am English, yes, but I primarily see myself as a European (in the sense that I identify with the inclusive and cosmopolitan values of Europe). I am also a Pagan, so I do not subscribe to the idea that British or European culture should be founded on Christian values (except where those are also universal humane values).
One of the many reasons that I welcome diversity in Britain is that, even ten years ago, it was very difficult to be openly Pagan, as many people assumed that it meant you were a devil-worshipper and/or a child abuser. One of the benefits of multiculturalism has been an increased recognition of the legitimacy of Pagan beliefs. Another reason is the massive improvement in our cuisine that has been brought about by the presence of other cultures.
Britain has always been diverse, ever since Roman times, when Hadrian's Wall alone had legions from Spain, Gaul, Germany, the lands along the Danube, Asia Minor, Syria and North Africa. (http://vindolanda.csad.ox.ac.uk/exhibition/people-1.shtml) Retired legionaries also settled in Britain. All these cultures lived happily side by side.
It is ironic that those who shout loudest about British culture being tolerant and inclusive are also the ones who vilify the supposed intolerance of Islamic culture - without bothering to look at the reality of what Islamic culture is actually like. The admittedly small sample of Muslims with whom I have discussed religion have turned out to be much better-informed about and well-disposed towards Paganism than many Christians I have encountered.
We need to focus on the shared values which underlie all our different cultures, whilst celebrating the diversity of customs and traditions. The reason that Britain has become more violent is because of the erosion of a sense of community and the social and economic alienation of many groups (not just extremists among the Muslim community, but other groups which have resorted to violence, such as racists and animal rights activists). This social and economic alienation is a direct result of the erosion of traditional economic infrastructure, such as the mines and factories. It is nothing to do with multiculturalism.
Integration is a two-way process, and requires both an inclusive attitude on the part of the majority and a willingness to be included on the part of the minority. However, one of the main difficulties in the way of Muslim integration is that British socialising revolves around alcohol, and alcohol is forbidden in Islam. If we are going to engage in dialogue, maybe we need to revive the coffee shop as a place to hang out.
Diversity is strength, monocultures are economically and biologically weak. A monoculture is slow to adapt and its homogeneity means it has no resources to cope with new threats and opportunities.