So, I came to the UK when I was 15, studied for over 10 years, got my citizenship. All legal, privately paid for. Incidentally, I worked as a solicitor for over 10 years, large part of my work was immigration law. There is no such thing as "uncontrolled" immigration outside the EU. When we were within the EU, we __chose__ not to enforce the rules. The arguments about it being non-practical (which is what Home Office told MPs select committee) are rubbish - Sweden, Denmark and Netherlands do so successfully from my personal experience. We could have done that too, __if we wanted to__. We just weren't bothered until the rise of UKIP.
Now about being poor. It took me 13 years, 4 of which working in Saudi Arabia, and a career change into software engineering, to make enough money to pay off my debts from school and start earning enough to live on without worrying about the next bill and looking after my wife and kids. Most immigrants I know do work hard. There is also a large swathe of people (immigrants and natives) who for variety of reasons rely on the welfare state. I do agree that welfare state should be downsized significantly. The reality, perhaps surprisingly, is that such a downsizing will hit the natives the most.