Even if you agree to be a donor, this doesn’t mean that you have to donate all of your organs and tissue. For instance, some people dislike the idea of donating their corneas, which unfortunately means there is a lack of corneas available for donation in the UK. Read more in this article from mirror.co.uk:
'Becoming a registered organ donor is a no-brainer - but they can’t have my eyes'
On the organ donation website, as well as the choice to opt out, there is also the option to specify which organs and tissue you are happy to donate, and which you would rather not. It is advised that you should also discuss this with your family, so they know your preferences if the worst should happen. This is important, as your family can override your decision if they are unsure it is what you want.