A record 3,706 organ transplants took place in the UK last year, an increase of 5% on the previous 12 months.
But NHS Blood and Transplant said there was still a long waiting list, with three people a day dying because of a lack of a suitable organ.
The refusal of relatives to allow donation often remains a key obstacle.
The doctors' union, the BMA, renewed its call for presumed consent, where all people are assumed to be willing to donate unless they choose to opt out.
There has been a steady increase in the number of organ donations in the past decade, and in 2008 a concerted effort began to boost the UK's rate, which lags behind those in most other European countries.
Many hospitals now have specialist nurses and transplant co-ordinators, and new systems which help identify potential donors and allow for an approach to families when death becomes likely.
The number of deceased donors reached 959 last year - some donating several organs - and there were 1,061 living donations.
There has also been an increase in the number of people volunteering to join the UK donor register, which hit the 17 million mark for the first time last year.
"We have made huge improvements to the way we work in hospitals," said Sally Johnson, director of Organ Donation and Transplantation at NHS Blood and Transplant (NHSBT).
"I'm glad these changes are reaping real rewards, with so many lives saved."
But there are still nearly 8,000 people on the waiting list for organ donations.
"Our work to promote the importance of organ donation must not stop as the need is increasing despite the rise in the number of transplants," said Ms Johnson.
In 2008 the government said it wanted to see the number of donations increase 50% by 2013. NHSBT says it is on course to reach that target.
At the same time ministers rejected a system of presumed consent, but some organisations believe this is still the best way to increase donation rates.
The BMA - British Medical Association - called for further debate on an "opt-out" system, and the British Heart Foundation said it would transform the number of available organs in one fell swoop.
"A heart transplant is a life-saving treatment for many patients and can give precious years to those who may otherwise have only weeks to live," said BHF policy director Beatrice Brooke.
The British Liver Trust said it was important not to be complacent.
The number of people on the liver transplant list increased 11% last year.
"Supply is simply not meeting demand, and liver disease rates show no sign of slowing down," said the trust's Sarah Matthews.
Public Health Minister Anne Milton called for more people to sign the donor register.
"We should all be aware of the difference we can make, or our families can make," she said. "A life lost can be a life saved."