It stands to reason given the country's population size and economic conditions, plus the fact that many of them can currently travel freely to the UK to live under Portuguese or Italian passports (as both countries offer these to just descendents rather than the more stringent citizenship rules of the UK). Even those who don't have them can arrive easy enough as tourists etc. and then drift into what is an undocumented activity.
Oh, that and women with dark skin and generous proportions, not to mention vivacious ways, tend to be popular with punters.
Sorry for the off topic but you haven’t got a pale idea about how stringent citizenship rules outside of the UK actually are.
In fact in 1981 the U.K. had to modify its citizenship rules as they were too relaxed compared with most of the ones in the EC. One example of that was what ended up in becoming the Windrush scandal, plus the fact that Commonwealth citizens had an easy ride on U.K. citizenship and thus the U.K. used to be a pass through for people to get a citizenship to open up the doors of the EC.
You will find that Italian citizenship in particular has never been easy to get. To begin with, jus sanguinis is based upon the notion that one of your parents has to be Italian citizen, which implies that the right to claim it has to be verified. That in itself is a lengthy process, especially when the last resort is to verify the central archives in Rome (using the last resort route implies in itself that the claim has little substance).
Plus, you should know that there must have been at least 7 million Italian citizens who emigrated to Brazil, Argentina and Uruguay in the 1870 to 1950 time span. Plenty of descendants to claim Italian citizenship.