Again identifying if people are marrying cousins would mostly be done on a "sign to say you aren't related basis"/self reported.
Many of the cultures where couples marrying is prevalent, would lie about it but also wouldnt have easily traceable documentation at hand. It would be partially based on people born in other countries, or people not overly engaged in the system eg travellers. Even using uk records is really tricky and time intensive.
Many of those cultures aren't also bothered about an "english" legal marriage. There's nothing to stop, or trace people doing faith ceremonies in non registered venues or their back gardens. My wedding in the eyes of my culture wasn't the day I had the registrars!
I think banning it will just lead to people lying about it. As a nhs worker its helpful to know if there is a risk, but id have no way of knowing if people lied, and they would be motivated to lie if they felt they/the baby would recieve different care
How many people here would consent (and pay for) the government taking dna in order to allow you to marry?
Besides its really not marriage people are worried about, it would be dna testing when pregnant. Then what would you do if you discover it was a cousin cousin child? Force an abortion? Take it in to care?
That's why its helpful to have targeted education and voices within that community, to stop faith leaders doing ceremonies where ever they are, so people that rent venues might not, so that the people themselves dont think its a great idea
Us all shouting it should be illegal and isn't it gross doesnt change a thing for them or the children other than reinforce an "us vs them" mentality where they become more closed off to nhs recommendations
Its bloody hard work to get people like traveller girls to stay in the system eg regular nhs support, schooling, health related classes. They dont need an ounce of encouragement to assume that we hate them all and want to persecute them