Are immigrants good for cities? Well yes, broadly speaking is the result. Life is much more complicated than blanket statements such as immigration is bad or good, but this study of the US cities is worth exploring.
Mind you, it wont be as such applicable in a country like UK which is far more densely populated. In this place, the line between the country and urban area is very blurred, specially with huge public transport networks. For example, now with the launch of the high speed Eurostar service, you can live in France and commute into work into UK. So be warned, but still, very interesting short essay on how immigrants impact natives in terms of their incomes and rents.