Around 16m people in the UK are on the organ donor register
Fear that doctors will not make every effort to save their life tops the list of reasons stopping people becoming organ donors, a survey suggests.
Many of those against or unsure about signing up are also worried about the level of respect that would be given to their body after death.
The NHS Blood and Transplant website survey of 5,000 people suggests more needs to be done to reassure donors.
About 3,000 transplants are done every year in the UK.
More than a quarter - 26% of the UK population - have joined the organ donor register but the number of patients on the transplant list is 8,000 and rising.
Around three people die every day while waiting for a suitable donor.
The vast majority of people responding to the survey said they were in support of organ donation and transplantation.
But, of those who said they were undecided or against, more than half said they were worried about how their body would be treated after death.
And one in five said they did not want to register as an organ donor as they did not like to think about death.
People want more information about what happens to the body after death and more reassurance that doctors will do everything they can to save someone's life.
Dr Paul Murphy, an intensive care consultant in Leeds and NHS Blood and Transplants national clinical lead for organ donation, said discussions on issues around death and donation needed to be more open.
"This survey shows that there may be questions playing on people's minds to which they need answers and reassurance.
"I cannot tell you just how much respect and honour my staff have for patients who donate organs after their death.
"Donors, and their families, are very special to us and we do everything that we can to maintain an individual's dignity throughout - why would we do any less when you consider the tremendous gift that they are making?"
He added: "Donation only becomes an option that we consider when death is inevitable, but it does need to become accepted as a normal part of end-of-life care if life is to go on for others when people die."
Dr Vivienne Nathanson, head of science and ethics at the British Medical Association, said it was encouraging that most people in the survey supported organ donation.
"We understand those who are concerned that being on the donor register could affect the care they receive but nothing could be further from the truth.
"Different clinical teams work with critically ill patients from those retrieving organs for transplantation.
"Doctors, nurses and others caring for the patient are working only for their benefit.
"We need to make sure that everyone knows about the systems in place to protect the caring relationship between the critically ill person and their doctors and nurses, so that still more people will sign the organ donor register."