Parents are much less likely to consent to donate a child's organs after their death than with other relatives, new figures show.
NHS Blood and Transplant (NHSBT), which oversees organ donation and transplant across the UK, said there were just 57 donors aged 17 and under last year.
The organisation said that for many children on the transplant waiting list, their only hope is the parent of another child consenting to organ donation at a time of personal tragedy.
Figures from NHSBT show that 48% of families supported organ donation on behalf of a child last year, compared with 66% agreeing for relatives of all ages.
The organisation said the figures have remained largely static over time.
But it warned that for some children a young donor is their only chance of survival.
Hearts and lungs need to be matched by size because of the limited space inside a child's chest.
For example, children waiting for an urgent heart transplant will wait two-and-a-half times as long as adults on the urgent waiting list.
Adults on the urgent list - for the most life-threatening cases - wait an average of 29 days for a new heart compared with 70 days for children.
NHSBT said that, in the last three years, 46 children have died while on the transplant waiting list. Of these, 30 were waiting for a heart or lung transplant.
Angie Scales, NHSBT's lead nurse for paediatric donation, said: "For many children on the transplant waiting list, their only hope is the parent of another child saying 'yes' to organ donation at a time of terrible personal grief.
"Organ donation can offer comfort to the families of donors through the knowledge that something remarkable came from their loss.
"There are many children alive today thanks to parents making the decision to donate when saying goodbye to their own child.
"Words save lives and we'd ask families this Organ Donation Week to talk about whether they'd want to save lives through organ donation if the unthinkable happened.
"We know that many children respond positively to the idea of organ donation so please talk about this important and lifesaving subject."
One family have been told that the only hope for their eight-month-old son is a heart transplant.
Harry Clarke, from Birmingham, has dilated cardiomyopathy and is being cared for at Newcastle's Freeman Hospital.
His mum Kerrie Short said: "We'd hope that family can look at it as an opportunity for their heart to live on through our son.
"Looking at him without his wires, you wouldn't know he was ill some days.
"Until you go through this and see how many babies are suffering with heart problems, considering organ donation probably doesn't even cross your mind but it's really important to have those conversations."
Children can join the NHS Organ Donor Register but their parents must give consent after they die.
Youngsters in Scotland can "self-authorise" from the age of 12.
Parents can also choose to add their children to the NHS organ Donor Register at any age, NHSBT added.
For more information visit: www.organdonation.nhs.uk