He would have a point if he were talking about Islamics, but most of the immigrants I see in the UK are far from problematic (of course, I don't live there). In the meantime, he has to acknowledge the fact that London has become, in many ways, a post-national city (much like New York and Miami are post-national cities in the United States).
I think that's true in many respects, but unfortunately Dalrymple's point isn't very clear. He wanders from his initial point (a country adapting its laws to the laws brought by immigrants) to another point, which is the responsibility of the immigrant to assimilate (into a nation, which as you point out, is now no longer a concept that has much meaning to many people).
I think a nation still must enforce its laws on anyone who happens to be within its purview: any immigrant, any person who has committed a crime within its borders, etc. I would have been happier if he had made the point that a country must still stay with its own legal structure, regardless of the attitude of the immigrant.
Our post-national cities, New York and Miami (particularly the latter), have populations that in general come from countries formed in the Greco-Roman/Judeo-Christian legal tradition of the West. They might have different cultural approaches, and they might need encouragement to learn English, but basically, the law is the same.
I think the problem is that London is receiving a large number of immigrants who don't come from this tradition or anything like it, and is making the situation worse by adapting to their legal system rather than making them adapt to its.