Your source doesn't establish this. It claims without evidence that Robinson's claims (and those of such partisans) originate in some particular report that I've never heard of despite years of keeping tabs on people who make those claims.
From what I can tell, the claims those people are making about rape in the UK generally have a much broader statistical basis; see e.g. https://archive.ph/jmS6q (the original Statista link isn't working for me, for whatever reason). Claims specifically about the gangs are based in things like https://en.wikipedia.org/wiki/Rotherham_child_sexual_exploit... (and note all the "See also" links). (But also see tremon's comment.)
The claim about conviction rates is missing the point entirely, that the Robinson protesters allege a wide-scale cover-up and bias against prosecuting the immigrants, ostensibly out of police fear of appearing racist.
> Where do you think your culture came from- thin air?!?
It's not mine (I'm Canadian), but yes, it literally did. Just like everyone else's. Thin air, and time. Time spent on doing things in the same way and noticing the patterns, and socializing.
> And so on and so on.
First off, infrastructure is not culture.
But the important thing is that all those events were centuries ago, taking place over the course of centuries. And in many cases they involved bloody wars and a whole ton of resentment. (Pretty understandable considering that the existing population, in each case, was trapped on an island.)
British culture was created by adapting ideas that were left behind in those conflicts. Just like every other culture is created by people with a shared identity picking up ideas, however they might be sourced, and forming a memeplex around them. That adaptation is what makes it British culture, and not "some combination of Roman, Anglo-Saxon etc. culture that doesn't deserve a name". That's why, for example, there was a Middle English, and eventually just more-or-less-modern English. A big chunk of that involved scholars independently studying Latin for their own reasons.
It's especially galling that you would whitewash the Norman invasions like this, considering the meaning and history of the two-finger salute. The same supposed "white supremacists" leading the charge in the UK still have less than pleasant banter for the French. The British literally developed culture by resisting foreign influence. (The whole "Britannia rules the waves" thing is also "culture", BTW.)
Anyway, none of these things involved the existing government consciously bringing in outsiders and completely transforming the population of major centers in the space of a generation or two. (Meanwhile, there are other parts of Europe — like the part DHH is from — that have not been subject to this. Should the EU be compelling them to follow suit or something?) This isn't about "locking in" culture; it's about understanding how the development (as opposed to displacement, or appropriation) of culture actually works.
> decided to stop and get a curry first
This is actually illustrative. Culture isn't just a curry recipe; it's the ritual of stopping for a curry with your mates. And eating it with English table manners, etc. Meanwhile, I can't fathom that the curry available in London actually reflects the cultural diversity of curry preparation within India; nor can I fathom that it hasn't been adapted in some ways to the local palate.
You can't just gift a cultural artifact to another people. Culture doesn't work that way.
(And if you think about what the word "colonialism" means to you, this should be obvious.)