You have only read one part of it if that is what you have taken from it.
In fact you are quoting selectively, not from the quote from the most recent study, but from one ( by the same authors) from 2008.
Lets quote some more:
" Well, the first thing to note is that a 10 percentage point rise in the proportion of migrants working in a sector – the amount needed to generate the “nearly 2 percent” wage impact is very large. Indeed, it is larger than the entire rise observed since the 2004-06 period in the semi/unskilled services sector, which is about 7 percentage points."
So even if you use the old data of 2008 the 10 percentage point rise never occured
Further: "we can calculate that the new paper implies that the impact of migration on the wages of the UK-born in this sector since 2004 has been about 1 percent, over a period of 8 years. With average wages in this sector of about £8 an hour, that amounts to a reduction in annual pay rises of about a penny an hour."
Sorry but your pulling bits of this out for confirmation bias and not reading the whole article.
" we have had a rise in the proportion of EU workers that is much bigger than 10 percentage points in these particular sectors, wouldn't you?"
No, this is explained above.
Immigrations has virtually no effect on wages of the lowest paid, and when accounting for increases in tax threshold has had no impact on real net wages.