The issue lies a lot closer to home though in that most likely one of the reasons why relatives refuse consent is because the deceased hadn't communicated their wishes beforehand. This isn't just about signing up to the register, it's about talking to your family about your wishes in the event of your untimely death. If they don't know what your wishes are, then they are the ones left with A, the shock of your sudden and unexpected death, and B, having to make the decision on something which had never previously been talked about at a time when there isn't time to be objective about such things or properly informed as time is of the essence.
"I am in agreement with Arf - told after the fact that your relative had donated their organs." that's not possible though as the deceased needs to be kept alive on life support until the organs can be harvested, which is done in theatre. Can you imagine the scenes if the person was simply wheeled away in front of grieving relatives because "We're going to take their organs now." You simply can't treat the living relatives that way. No time to say goodby, no time to be with their relative as they passed away having turned off the life support. Bear in mind that we're generally talking about grieving parents/partners/children here.
I'm afraid that the onus here lies with the organ donor, to make their wishes known to their next of kin at the point they sign up to the register. If you don't make your wishes known and your next of kin override them, then that is unfortunate, but communication is the key here. (And I am on the donor register and have told my family of my wishes.).
I do however find it bizarre that there are people who have said that they don't believe that your next of kin should have decision powers over your body yet are happy to want an opt-out system which essentially makes your body the property of the state unless you actively tell them otherwise. So you trust the state over your family?
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I am completely and utterly against an opt out system, and it seems that the Welsh are in agreement as thousands of people had already opted out on the first day and are continuing to do so. I would far rather my family made the decisions than that I lose all bodily autonomy and become the property of the state on my death. I am currently on the register, but if opt-out ever becomes law in this country I will be opting out.