What complicates any legislation is that a one-off first cousin marriage has one level of risk, which is higher than that of two unrelated people marrying, but a marriage where the family tree shows several generations of cousin marriage will have a different (and higher) level of risk.
It blows my mind somewhat that it's advised when breeding animals that any co-efficient of inbreeding (COI) above 5% increases the risk to a potentially unsafe level - not just the risks of genetic illnesses, but also cancer and auto-immune problems, and also potential impacts on fertility and resistance to infection.
First cousin marriage has a COI of 6.25%. That alone would bother me if one of my DC announced an intention to marry one of their cousins.
Arguments about high rates of disability, child mortality etc in places like Bradford that also have high rates of consanguinity don't take into account the fact that those areas - and particularly the communities in those areas that practice cousin marriage (in Bradford, Pakistani Muslims, but in other areas it will be other cultural groups) - also have high levels of socioeconomic deprivation, which has a known impact on health outcomes, including at an epigenetic level
The Born in Bradford study found that socio-economic status alone had no impact on the level of birth defects. Consanguinity is an avoidable known risk, and the consequences can be devastating and are so sad for both the children and their parents.
Edited for typos and to add a bit.