In a procedure described as a milestone in neonatal care, a six-day-old baby girl's kidneys and liver cells were given to two separate recipients after her heart stopped beating.
Experts argue there is potential for more life-saving donations, but say current UK guidelines are prohibitive.
An official review is expected by the Royal College of Paediatrics and Child Health this year.
Writing in the journal Archives of Diseases in Childhood, doctors describe the case of the baby girl who was born in extremely poor health.
Tests suggest she had been starved of oxygen before birth and despite resuscitation had profound brain damage.
Doctors at Imperial College NHS Trust in London say in an act of "extraordinary generosity" her parents agreed that her organs could be donated once her heart stopped beating.
Her kidneys were given to a patient with renal failure.
And in a separate operation her liver cells were transfused to someone with a failing liver.
Medics said the surgery was incredibly difficult and intricate. The kidneys at this stage of life are around 5cm long.
Doctors hope the donated organs will completely transform the lives of the recipients.
They have not disclosed any further information about the patients who were given her organs. But they say the neonatal organs could be donated to young babies, children or even adults.
Prof James Neuberger of NHS Blood and Transplant, said: "We are pleased the first transplant of organs from a newborn in the UK was a success and we praise the brave decision of the family to donate their baby's organs.
"The sad reality is for everybody to get the lifesaving transplant they are desperately in need of, more families who are facing the tragic loss of their young child will need to agree to donation."
Dr Gaurav Atreja, who was involved in the transplant, told the BBC: "This turned out to be a positive thing for the family.
"They could see something positive out of a negative experience.
"We hope that neonatal units across the UK will actively start thinking about this noble cause."
Official waiting lists suggest some 15 infants under the age of two currently need organs across the UK. But experts say the number may be higher - many do not make it on to the list because of the scarcity of options.
A handful of donations have taken place involving infants who were nearly a year old.
But NHS Blood and Transplant says for young babies requiring transplants, the size of the donor organ is often critical to success, meaning organs from older donors will not always work.
Despite newborn organ donations being performed in the US, Germany and Australia, doctors say guidance about the diagnosis of newborn death in the UK may hamper life-saving operations.
Unlike some other countries, clinicians in the UK are not allowed to declare brain death in a baby under two months of age.
The Royal College of Paediatrics and Child Health is to review this and report back in March.
NHS Blood and Transplant says it welcomes any clarification that will ensure organ donation can take place where appropriate, "particularly where parents of potential donors are keen to have something good come out of their own personal tragedy".
Doctors have performed the first organ transplants from a newborn in the UK.