Hundreds missed out on organ transplants in one year
NHS Blood and Transplant said that across the UK, three families a week said no to organ donation because they did not know the wishes of their relatives.
It said that when families are left to make such a decision, some decide it is safer to say no.
The organisation has encouraged people to talk to family members during Organ Donation Week, which runs from today.
The reluctance to talk about the issue is contributing to a deadly shortage of organs, NHSBT said.
Last year, 457 people died while on the active transplant waiting list and a further 875 people were removed from the list, mainly due to ill health.
On August 25 there were 6,414 people on the waiting list.
The parents of a four-year-old who died on the waiting list have urged people to discuss the topic.
Aoife O'Sullivan from Leigh-on-Sea in Essex died in March 2016 while waiting for a heart transplant.
The youngster was in need of a new heart after suffering heart failure from restrictive cardiomyopathy - a condition which made her heart muscle rigid.
After she died, her parents chose to donate her kidneys.
Michelle O'Sullivan and Neil Forsyth, from Leigh-on-Sea in Essex, have backed the NHSBT campaign to encourage people to talk about their wishes surrounding donation.
Ms O'Sullivan said: "Neil and I take comfort from that fact Aoife has given somebody more time with their loved ones. We feel very proud of Aoife.
"I would say to people 'put yourself in the shoes of someone waiting for a transplant'.
"If you are willing to accept an organ donation, it is only right that you should be willing to donate the special gift of life to another family."
Anthony Clarkson, assistant director of organ donation for NHSBT, said: "It's a tragedy, hundreds of people are dying unnecessarily every year waiting for transplants.
"We know that if everyone who supported donation talked about it and agreed to donate, most of those lives would be saved.
"This Organ Donation Week tell your family you want to save lives. A few words now can make an extraordinary difference. It will also make things much easier for your family to make the right decision.
"If you want to save lives, don't leave it too late to talk to your family. If you want to be a donor, your family's support is still needed for donation to go ahead, even if you are on the NHS Organ Donor Register.
"And if you are unsure about donation, please ask yourselves as a family, what would you do if one of you needed a transplant? Would you accept a lifesaving organ? If you'd take an organ, shouldn't you be prepared to donate?"