The number of people donating organs after their death has risen by 50 per cent since 2008, according to new figures.
The increase has in part been credited to the network of specialist nurses who approach bereaved families in hospitals.
But the NHS Blood Transplant (NHSBT) says more still needs to be done to actively boost the number of people on the donor register.
One of the recommendations made by the government’s organ donor taskforce is to change the law to ensure relatives cannot override the wishes of individuals who have elected to become donors before their death.
Sally Johnson, NHS Blood and Transplant’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.”
Last year 125 families overruled an individual’s intention to donate, despite their names being on the NHS register list. While the law does not give relatives the power to prevent donation, doctors are reluctant to press grieving families. As a result 45 per cent of cases are overruled by relatives.
According to Kidney Research UK each donor has the potential to help nine people through donation of a heart, lungs, two kidneys, pancreas, liver and small bowel and two corneas.
In 2008 ministers accepted the recommendations of the Organ Donation Taskforce, which included:
Since then the numbers of donors has seen a rise. Five years ago, 809 people who died donated organs. In the last five years there has been a 50 per cent increase in organ donors, with more than 1,200 people in the UK donating their organs during 2012-13. As a result transplants went up from 2,385 to 3,112.
Another proposed change is whether to have an opt-in or opt-out system introduced.
The Welsh government is hoping to bring in a system of presumed consent in 2015, where people must specifically opt out if they do not want to be considered.
So far there are no similar plans in England or Scotland, but some medical professionals say depending on what happens in Wales, this could set the benchmark for the rest of the country.