The number of people donating organs after death has increased by 50% in the last five years, but the NHS is calling for more to be done.
Over the last 12 months more than 1,200 people in the UK donated organs, NHS Blood and Transplant (NHSBT) said, helping to transform 3,100 lives.
But doctors say a transformation in donor and family consent is still needed, as many families refuse to consider the possibility of organ donation when a loved one has died.
Despite the increase in organ donors, the numbers of families refusing to grant consent remains among the highest in Europe, and the NHS Blood and Transplant (NHSBT)
Sally Johnson, NHSBT's director of organ donation and transplantation, said: "Although I am delighted that we have made such big advances in the UK, we can and must do more.
"We need a transformation in donor and family consent to organ donation because the UK's family refusal rate remains one of the highest in Europe.
"Without that, there is only a limited amount more the NHS can do to offer further hope to those on the waiting list for an organ transplant."
A new strategy is to be launched this summer that will build on the 2008 recommendations of the Organ Donor Taskforce and encourage more people to donate organs.
The sharp rise is largely due to the creation of a network of specialist nurses who support bereaved families and discuss the possibility of organ donation with them.
Specialist nurses are one of a number of recommendations made in 2008, following a decade of almost no increase in the number of donated organs.
The taskforce also pushed for the creation of specialist organ retrieval teams and wider promotion and campaigning around the importance of organ donation.
The recommendations led to an increase in organ donors across the UK between 2007/8 and 2012/13 - rises of 49.1 in England, 15.6% in Wales, 74.1% in Scotland and 81.8% in Northern Ireland.
"This is an outstanding achievement that few thought possible at the time this ambition was set," said Bill Fullagar, chairman of NHSBT.
"It is the result of the hard work and dedication of staff in hospitals and communities across the country.
"We must also share our heartfelt thanks with every family who, at a great time of sadness, supported their loves one's wish to donate their organs and transform the lives of up to nine other people."
The increase in donated organs has led to a 30.5% boost in the number of people receiving a life saving or enhancing organ transplant in the last five years.
Professor Anthony Warrens, professor of renal transplantation surgery at Barts Health NHS Trust and the Royal London Hospital and president of the British Transplantation Society, praised the NHSBT for the increase in organ donors.
He said: "There can be few greater achievements than to have given life to those who were on the verge of death - but that is the reality of this achievement.
"Data show that an individual who donates his or her organs after death gives the recipients an aggregate of an additional 56 years of life. And despite the sadness of the moment, this usually becomes a major comfort to bereaved families as time passes."
Dr Paul Murphy, an intensive care consultant in Leeds and NHSBT's national lead for organ donation, called the 50% increase a "landmark event in donation and transplantation for the UK".
"But we can and must do more, because patients continue to die needlessly waiting for an organ transplant.
"Now we have the foundation to push on and create a donation and transplantation service that we can be proud of. Too many families continue to say no, sometimes even overturning their loved one's commitment to donate after death."