Nearly 30 years ago my sister was knocked off her bike as she cycled to work. She hit her (unhelmeted) head on the kerb and died of her injuries 2 days later.
My parents were approached about donating organs and at first, my mother couldn't bear the thought that her daughter, badly bruised by the accident and further damaged by the three operations undertaken to try and save her life, would be further mutilated by surgery to remove organs.
But then we found a kidney donation card in her wallet and all the rest of us were very positive about donating organs and my mother agreed.
Her kidneys returned two young men, fit and well to their families, 15 year old girl received her kidneys. Her heart had been damaged and could not be used.
In that darkest of dark times, the knowledge that our loss had brought life the three people was immensely comforting.
There was never a moment when we thought that her organs were more important to the doctors than her life. She was kept on the life support system for two days after death was confirmed, to make sure that there could be no doubt about her death and the treatment she received before death was also the best available.
I have also experienced a close friend dying because a matching liver did not become available in time.
I am, nevertheless a little ambivalent about presumed consent, but do believe that if someone has expressed a willingness to donate organs and/or carries a donor card, it should not be possible for a relation or next of kin to refuse to let the organs be taken after death.