Try to understand what something means before you mindlessly parrot it. The article I linked to shows that there is no correlation, or even negative correlation between immigration and unemployment. And that actually proves pretty conclusively that there is no causation.
OK, my comment was glib, but I do understand the meaning of "correlation is not causation". The link you provide attempts to refute the argument that "immigration causes unemployment". You correctly point out that no correlation was found in the case of the UK. My point (and hence my rather glib comment) is that this lack of correlation tells us nothing about causation.
Importantly, taking unemployment overall conceals that fact that certain portions of the workforce (i.e. the young and low paid) are disproportionately affected by a rapid influx of young tradesmen and low-skilled workers.
