Marrying your first cousin in legal in the UK. Always has been.
It's not a matter of legality. It's a matter of what culture is actually doing it, and the strain on the healthcare system as a result. From the video:
"Here in Bradford, where the [name of Pakistani family] live, 75% of Pakistanis marry their first cousins. Anywhere between 4 and 10% of the children in these families will be born with genetic abnormalities. And these illnesses are often fatal. One third of children with diseases caused by recessive genes will die before they turn five.
Over in Birmingham, home to one of the largest Pakistani communities in Britain, 50% marry their first cousins. The children born into these families are ten times more likely to be born with recessive genetic disorders, and one in ten of those will die in infancy or suffer a chronic disability.
A major report published in 2008 shows that one third of all children suffering from rare genetic diseases are British Pakistani, yet they only make up 1.5% of the total population.
Cousin marriages have been a long-established cultural tradition amongst many British Pakistani families. But it's not just within this community. In the past, the British royal family married their first cousins, too. Today, though, it is mostly Pakistani, Bangladeshi, and some Middle Eastern and East African families that continue the custom."
Europe taking immigrants from outside Europe? Not really a Brexit issue, not directly. We will still have the same problem.
It's a legal requirement of the EU to allow free movement within the EU. Merkel threw open the flood gates to refugees. The only hope for the UK to restore sanity to migration is to enact their own policy outside the EU.
And swarms flooding in? The population is barely around predictions of the same made in the 1970's. We're not "swarmed" anywhere. At all. But observer bias, and all that.
What's happening is population replacement. The natives have low birth rates, the immigrants high ones. Entire white communities have been displaced by immigrants and have become minorities. And it's only going to get worse with the new flood of immigrants.
But what really shows me I'm wasting my time is that you've linked to an anti-Muslim article as an example of why Britain should get out of the EU on the basis that "immigrants are Muslim" and "Muslims are trouble" (paraphrasing, but that's basically your gist right?)
Of course it's my gist. But rather than address the problem, you just pretend it's not there while touting only the benefits of immigration. By the way, I gave two links, one was to a video describing the British Pakistani problem of first cousin marriages. The second was to a respected polling organization that showed what Muslims think in different countries -- you know, the ones where massive migration into Europe is coming from.