Government advisers have recommended a radical overhaul of the UK organ donor network in a bid to double the number of organs available for transplant.
By recruiting twice as many transplant co-ordinators and creating 24-hour organ retrieval teams they hope to emulate Spain's successful model.
A system of "presumed consent" in which everyone is a potential donor unless they opt out is also being considered.
Gordon Brown has backed the opt-out idea, which is still under discussion.
Writing in the Sunday Telegraph newspaper, the prime minister said a system of "presumed consent" - where hospitals could take organs unless a person had explicitly opted out before death or their family objects - could save thousands of lives.
"A system of this kind seems to have the potential to close the aching gap between the potential benefits of transplant surgery in the UK and the limits imposed by our current system of consent," he wrote.
A government taskforce set up to examine the donor shortage and consider the issue of presumed consent will report in the summer.
Meanwhile, the Scottish Government said it was committed to implementing the reccomendations in the taskforce report, which they said could result in an extra 120 transplants a year in Scotland.
Mr Brown, who carries an organ donor card, said he hoped the measure could be introduced this year.
Lib Dem MP Dr Evan Harris, chair of All-Party Kidney Group and member of the BMA Medical Ethics Committee, welcomed Mr Brown's comments.
"Under an opt-out scheme donor's real wishes will be more often respected, more lives would be saved and grieving relatives will be spared the experience of making the wrong decision at the worst time," he said.
Mr Harris said too many people were "needlessly dying while waiting for organs".
However, several patient groups, including Patient Concern, are against a system of presumed consent, arguing that it is not up to the state to decide what becomes of people's bodies when they die.
Joyce Robins from Patient Concern told BBC Radio 5 Live presumed consent turned volunteers into conscripts and that proposals did not tackle the problem of donor shortages.
"Presumed consent is no consent at all. We've worked for years to get a system of proper, informed consent in the health service in this country and Gordon Brown is willing to throw it all out of the window," she said.
There are more than 8,000 people waiting for organ transplants in the UK - a figure which rises by about 8% a year. And one person dies every day because of a lack of organs.
So far, the taskforce has made 14 recommendations for tackling the backlog.
They include doubling the number of transplant coordinators in the NHS to 200 and employing and training them centrally rather than by individual trusts.
Coordinators identify possible donors, talk to bereaved families and inform the national transplant list.
Dedicated organ retrieval teams available 24 hours a day would also be established to work closely with the critical care teams in hospital.
The proposed system is similar to that in Spain where they have three times more available organs than in the UK.
It is expected the measures could result in a 10% increase in the consent rate for donation which currently stands at 60%.
The taskforce says an extra 1,200 transplants could be done each year, which it says could save the NHS more than £500m over 10 years.
This is because dialysis for kidney failure patients costs £25,300 a year, whereas a transplant costs £45,900 initially followed by annual treatment costing £7,100.
Health Secretary Alan Johnson said: "Last year around 2,400 people in the UK benefited from an organ transplant, but more than 1,000 people die every year waiting for a transplant.
"These recommendations are an essential first step to improve the systems supporting organ donation."
Chris Rudge, director of UK Transplant, said there were weaknesses in the current system that needed to be addressed, saying lack of family consent meant four out of 10 organs considered suitable for transplant were not being used.