If May wants to cut immigration down to tens of thousands she'll need to stop the right of uk citizens marrying someone from the old country (preferably second cousins) in Pakistan or Bangladesh and bringing them ( and the partner's wider family) over here. They usually don't speak English, live in majority areas, so are able to live separate lives.
I've said before living in tower hamlets, the more Eastern European christians that settle locally the better. They integrate much better and their kids will grow up as English as mine. Some of the other third world immigrants won't; I'm not saying they are all Islamist nutters, some are pleasant - but it's hard to tell what they are like if they only speak Bengali and have hijabs. If we are going to choose who comes here - let's give it some thought.
I lived in Tower Hamlets between 1988 and 2013 (Isle of Dogs). I agree with you. It's easier for white Eastern Europeans to integrate because they don't look so different and their kids get included in whatever the other white British kids are doing. If they're Christians or atheists, that also makes it easier. It doesn't make sense (to me) to permit people to settle permanently in the UK if they don't speak English to a certain level of competence. However, some of those white Eastern Europeans will be Muslims not Christians - but they'll integrate relatively easily too. When you see their kids on the bus, you'll never know who they are or where they came from.
I agree with your observation about sub-continent marriages, too. In East London, running my motorcycle school, I came into contact with many people who were British-born of Bangladeshi parents who ended up in arranged marriages with someone from "back home". They were always British women who had married men from "back home" who came to live and work in the UK. I don't think that it was exclusively that way round, it's just that the men coming here to live would be motorcycle training customers and most Bangladeshi women marrying British men will not be - so I only got to see it from that perspective. The grasp of English by many of these men was poor. Their British wives would phone in and make the bookings and sometimes accompany them to the training session to be the interpreter. (You don't have to speak English, nor understand it, to get a driving licence).
I also came across many young men from abroad who were taking their CBT so they could legally ride a scooter and deliver fast food. They were in the country on student visas, but not really what I would call student material. I've no idea if they went to classes or if the school that sponsored their visa was a real school or just a front to get people into the country.
We do have areas where 1st generation immigrants live within their own bubble, and it's not to the same cultural reference points as me. People coming to a new country tend to congregate with others like them. We've got Greeks and Turks and Cypriots - Muslim and Christian - living in certain parts of North London, for example - but you'd never know who they are until there's a football match.
British-born children of Bangladeshi heritage are growing up in areas where they don't mix with people outside their own "back home" culture except when at school. In Tower Hamlets, some schools are now almost exclusively attended by these kids. So they're not getting exposure to other people from other cultures at school, either.
What they are getting exposed to is the drip drip drip of a specific type of Muslim fundamentalist view of the world, with objectives driven by hate and a desire for political influence that they will not be able to get by other means. It's these people that need to be identified and stopped - without turning them into martyrs that result in us getting more people willing to become terrorists in their own country.
How do we convince these 2nd generation Brits that this
is their country and they have a stake in it?