I live near the school featured in Educating East London. It is a very cosmopolitan area and over the last six years or so a growing number of Eastern European people have moved here.
I have found that people who come from other countries are generally no better or worse than those that already live here and, from what I can see, the majority are employed. They often work as carers, cleaners and other low paid and demanding jobs that (perhaps understandably) others are less keen to do. Those working as builders, plumbers, etc., we have found to be highly skilled and hardworking.
Having a pool of people to do the most demanding jobs for the least amount of money, may in the short term appear to benefit everybody in that it keeps the cost of services and goods down. In the long term, it accelerates the "race to the bottom" where wages for all but the highest paid are held down. That is not the fault of immigrant workers but of a government which is in the main bankrolled by big business which benefit from people from other countries who are willing to work for very low pay. I think it's also the fault of previous government who thought that by encouraging public/private ventures and using a "softly softly" regulatory approach the economy would thrive and everybody would benefit.
Businesses are dependent on the social and logistical infrastructure of a country. But - despite the growing pressures on housing, healthcare, education, transport, etc. - they are very unwilling to pay their taxes towards it. I think that is the root of the problem, and the issue of immigration is being used to divert attention from it.