Perhaps at the moment, yes, but I'd say an influx of an additional 80,000 legal workers at negligible cost would probably have a more direct and effective negative impact upon the wages of the least skilled (or, probably more true, the current and long term employment prospects for them).
Yes that is definitely true but then you can't really do anything about a worker who is here legally and is willing and able to work for less, apart from continually raising the minimum wage to increasingly uncompetitive levels.
I think I may have wandered off topic a bit...