The government is working towards 25 million registered donors by 2013
The UK has rejected an opt out system for organ donation for now and will instead rely on a £4.5 m public awareness campaign to boost voluntary donor numbers.
But prime minister Gordon Brown said he was not ruling out a change in the law on organ donation in the future.
What is the current system and why is there talk about changing it?
Currently, people in the UK must sign up to the organ donor register - or their families must agree - before their organs can be used.
It is normal practice to let relatives know if the person has opted in and doctors can decide not to proceed if faced with opposition from relatives.
However, there is a gross shortage of donor organs which has sparked debate about whether this system should be changed in order to boost donor numbers.
There are more than 8,000 people waiting for organ transplants in the UK - a figure which rises by about 8% a year.
Only 3,000 operations are carried out each year, and every year, 1,000 people in the UK die after waiting for a transplant.
Most of the countries with the highest rates of registered donors have an opt out system where consent to donate an organ is presumed unless a person formally states otherwise.
This has led experts to question whether the UK should follow suit.
How would presumed consent work?
Many European countries have a form of "presumed consent" or "opt out" system. This means doctors can remove organs from every adult who dies, unless a person has registered to opt out.
In some countries, such as Austria, this applies even if relatives know that the deceased would object to donation but had failed to register during life.
In others, like Spain, the relatives of the deceased should be asked for their agreement.
Some countries also exempt people who belong to certain groups that are defined by law as being against an opt out system - such as Muslims in Singapore.
Why have experts rejected presumed consent in the UK?
The task force charged with looking at this option, which had gathered over 400 pages of evidence from across the world, found little evidence that presumed consent would increase the number of organs available for transplant.
The task force members said that although a system of presumed consent in Spain had been followed by a rise in organ donation, that rise was not thought to be down to the switch, but rather down to better public awareness of donation and confidence in doctors.
They heard from health professionals that there was a significant danger of presumed consent eroding patients' trust in doctors and put potential donors off.
Brazil adopted a presumed consent law in 1997, with opt out denoted by a note on an ID card or driving licence. The law had to be repealed in 1998, principally because of mistrust of government and accusations of body snatching.
In France, which also has a system of presumed consent, there was an incident in 1992 in which corneas were taken from a 19-year-old road traffic accident victim whose parents had consented to only limited organ retrieval.
The task force said the opt out system also had the potential to undermine the concept of a gift freely given, which is known to be important to both donor families and organ recipients.
It would also be a costly and technically demanding to system to introduce. And there would need to be legal provision relating to children and those lacking capacity to opt out.
What is the task force recommending?
It says to boost the number of registered donors the UK should follow the example of Spain and the US and employ celebrities to raise public awareness.
The US uses basketball players, while Spain uses the Seville football club to front its campaign to recruit donors.
The government in England has earmarked £4.5m funding over the next two years for a major publicity campaign.
The Spanish experience also shows increasing in the number of donor coordinators who work with bereaved families, and the number of specialists who retrieve organs can have a significant impact on donor rates.
Each NHS Trust in England is to appoint an organ donation champion to discuss organ donation with families as part of all end of life care where appropriate.
A UK-wide network of dedicated organ retrieval teams will also be established to ensure timely and high quality organ removal from viable donors.
Training is already in place for donor transplant coordinators and an additional 63 coordinators will be recruited across the UK by 2009.
NHS Scotland has been asked to produce new awareness-raising material to inform people about the existing legislation.
The government hopes these measures will increase the number of registered donors to 25 million by 2013.
If not, Gordon Brown said he will revisit the idea of presumed consent in England.
Scottish health minister Nicola Sturgeon has made the same commitment.
However, Welsh Health minister Edwina Hart, has rejected the all-party Welsh Assembly report when they decided against presumed consent after weeks of evidence and is still pressing ahead.