But there's another, less obvious reason, too: the seat belt. The decline in donors to around 800 a year is also caused by safer driving and a decrease in fatal road accidents.
If the rate of transplants is ever to change, attitudes will have to shift radically. National Transplant Week begins tomorrow, when we will all be asked to consider donations. Gabe Wilkinson, chairman of Transplants in Mind (TIME), says: "Unless we can get more people to accept organ donation as an everyday subject and take action by telling their friends and family, joining the Organ Donor Register or carrying a donor card, nothing will change - people will continue to die for want of an organ".
Tonight, a BBC1 documentary, Giving Life, marks the start of the campaign to encourage more donors. Here are some of the stories of the people featured:
52, lives in Crook Hill, Warwickshire
"My son died eight years ago in a cycling accident. I knew he felt strongly about being a donor - we had a discussion and I remember him saying, if anything happens I want to give my organs.
But then, when my partner first suggested it to me after the accident, I said 'No'. I couldn't think of doing it. Your first thought is, 'this is my child and no one is going to take his kidneys'. At that point I couldn't accept that Andrew really had died. The next day, though, they confirmed it and a consultant asked. Then, somehow, it was easier.
I knew it was what Andrew would have wished and that helped. I realise it is difficult for the doctors but I'm so glad I was asked. They used both his kidneys, his liver and his heart. I said I wanted information about who'd received them and the hospital told me their age and gender.
Two and a half years after Andrew's death, I heard from his heart recipient, Derek. We talked on the phone and met in August - on Andrew's anniversary. It was very strange and so emotional that Derek and I couldn't speak at first. It gave me such a good feeling and helped me with the grieving process. Meeting him was one of the best things I ever did. As a result, Andrew's memory goes on and it really is a tribute to his life."
(right) 55, from Doncaster, was the recipient of Andrew's heart
"I'll never forget 19 August 1991; I was playing with my son. The phone rang; it was the hospital saying 'Pack your bags, you're getting a transplant tomorrow morning'. A day later, I had a new heart.
It all started in 1988 when I had a massive heart attack. I had to have quadruple bypass surgery and although it was successful at first, four months later the bypasses folded and I had to go back to square one. The doctors told me I couldn't have any more open heart surgery because I probably wouldn't live through it and they gave me about a year to live. I was told a heart transplant was the only other option, although there was a 5 per cent chance I'd die on the operating table. I knew that I didn't have much choice at that stage.
After the operation I made a fast recovery. Later I felt I had to get in touch with the donor. I wrote to her and a month later she replied. Then I phoned her; we talked for a few minutes and I agreed to call back. The next time she heard from me, she was over the moon and some time later we decided to meet up. It was August 1995 on the anniversary of Andrew's death and we met in a lorry park near East Midlands airport.
I arrived first and saw her drive up. Then she got out of the car and just stood there. We couldn't speak a word and my wife had to break the ice and say, 'Let's go for a drink'. I told her how much I appreciated what she had done and she showed me a photograph of Andrew. We both gave each other presents and it was a very emotional meeting.
I knew I had to make contact with her even though counsellors had told me to be cautious about calling her. I'd heard that the donor was a young boy and felt it was such a shame that he'd died so young. Writing that card to her was the hardest thing I've ever had to do but it was the best decision I made - we still phone each other and I know there'll always be a deep friendship there."
(above) 32, lives in Oldbury, Midlands
"When I was young I was a sickly child. Eventually, the doctors discovered I had a hereditary illness and was suffering from kidney failure. At the age of 14, I went into dialysis and two years later I had a kidney transplant which didn't work. Two years after, I had a successful transplant that lasted for nine years. In that time I married and had two daughters; I led a completely normal life, I'd never been that well before and it was all completely new to me. Suddenly I could walk down the street without getting breathless - life was so different.
I was 27 years old when my kidney failed again, and the second time around it was much more devastating. I had had a taste of what life could be like; of feeling active and well. And then it was all snatched away from me again. Last October, I had a transplant that failed and now I am still waiting for another one.
I try not to give up because of the children, and my husband is incredibly supportive - he does everything for me. But it's a constant struggle and I often feel like giving up. Dialysis is gruelling; four hours a day, three days a week. But it's more like six hours once you've taken the needles out and stopped the blood.
The next day I feel tired and lethargic, then it's time to go through it all over again. The simplest tasks exhaust you. Although a transplant could change my life, I don't feel anyone should be forced to give their organs legally - I'd hate to think someone was holding a gun to my head and demanding my daughter's organs if she died. Organ donation is a gift of life and you shouldn't force someone to make that decision."
DR JOHN BUCKELS
Transplant surgeon, Queen Elizabeth Hospital, Birmingham
"The overriding ethical decision is to make sure you choose the right person for the transplant; it's a bit like an investment. You want the best return. When a doctor asks about organ donation it's what no relation or loved one ever wants to hear. But obviously, from the point of view of the doctors, we've got to act as advocates for our patients.
What I would say is, if it was the other way round - if you were in need of a transplant - you would very much want it. In other countries the laws are much stricter. In Singapore, for instance, unless you're registered as a donor, you won't receive a transplant.
People have to face up to certain issues; when they're offered a longer life they'll always say 'yes'. Yet about one-third of families, when put in the acute situation of being asked about donation, will say 'no'. It is such an awful time to be asked and they do have to make an on-the-spot decision. Which is why there are some families who are never approached but wish they had been - and many others who said 'no' at the time and now wish they'd said 'yes'."
'Giving Life', presented by Sue Lawley, is on BBC1 tonight at 6.10pm.