In my experience (overall) integration becomes less likely as immigrant populations increase. Whilst you have more people integrating well because there are more to integrate, the proportion that are integrating well drops.
One of our managers is Polish and she's been here for almost as long as Poland have had free EU movement and feels it's becoming a barrier to employment for us. According to her she had no choice but to integrate - she had to speak English or not speak, she had to have English friends or no friends, she had to buy English products or no products.
In her opinion that no longer applies to more recent Polish immigrants. Some of the staff that are not learning English at all live in a house full of Polish people rented from a Polish landlord. They buy Polish products in Polish shops, they drink in Polish pubs and clubs with other Polish people.
Those people are comparatively rare but on the increase and that can't be good for either population. A similar situation happened with a lot of the Asian staff we have in Birmingham. The difference being, that because they have such a patriarchal culture, it's only the wives that didn't integrate, the men still did. The next generation seems to have a fairly even split - to the point where some of the people who work with us are fully integrated but have a sibling that cannot speak a word of English.