In some cities in the north of England lack of integration is a serious problem, though, and it relates to people of Pakistani heritage. There are ghetto-like areas (as there are in US cities for many ethnic groups) where they live and white Brits don't. Some immigrants do not speak any English, especially females, and there is no pressure on them to learn it.
My home town is one such. The town centre is completely changed—there is just one hotel and no pubs at all now. Many shops have closed. The place is absolutely dead in the evenings, even on a Saturday night, and it's uncomfortable to walk around during the day, especially for white girls and women—in fact there are very, very few white shoppers altogether. My own family never go there now; my DNs and DGNs were leered at and harassed constantly, as were their female friends, even if they were in groups, so they simply stopped shopping there.
This harassment would be unacceptable from men and boys whatever their religion or the colour of their skin, of course, but my sisters and I and our female friends never suffered such a degree of unwanted male attention in the past in the town centre. All men and boys need educating about their treatment of women and girls, I fully realise that. Maybe harassment is generally more widespread and intense than it used to be, in all communities? Is this another effect of the easy availablity of violent porn and the general pornification of women?
It's true that in the past many immigrants set up their own businesses (e.g. the refugees from Uganda, many Jewish immigrants). They had to do this, to survive and thrive. Jews have long had to cultivate portable skills so they could survive whenever the rest of the population decided to expel or expropriate them (again). Pakistanti-heritage people have also set up businesses (they can get loans without paying interest, which is always an advantage); they have even achieved a monopoly in some types of service (e.g. taxi firms, food delivery). This sort of enterprise contributes to the economy, but is not the same as integration.