It isn't quite that simple of course. To start with, only one per cent of people will die in circumstances where organ donation is possible. Obviously you can't donate organs if you've died of some serious illness affecting the whole body, or if your organs have been damaged in (say) a car accident, or if you've died abroad and it would take time to return the body to the UK.
Also my family would have to be consulted about donating my organs, and if they objected my body would have to remain intact. Doctors won't proceed if the family objects, however useful my organs might be (though I see that next of kin don't have the legal right to veto your decision).
My immediate family is my sister, my brother in law and my niece. but whether they count as family for the purpose of consultation isn't clear.
So although theoretically it's entirely my choice to allow my organs to be donated, in practice my family can overrule me and doctors' hands are tied. I don't agree with that at all. I don't see why my family should have any say in the matter, since it's my body and not theirs. It's especially perverse when over 7,000 people in the UK are waiting desperately for life-saving organ transplants.
I would like to think that someone in urgent need had been given one (or several) of my organs and had a new lease of life, and that my body hadn't simply gone to waste.