The report of the Task Force said there was insufficient evidence to support the change, which would make people automatic organ donors unless they choose to 'opt out.'
Instead it is suggesting a £4.5 m public awareness campaign to boost voluntary donor numbers.
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. But the panel didn't seem impressed.
Elisabeth Buggins, head of the UK Organ Donation Taskforce told BBC Breakfast: 'The Government asked us to look at presumed consent. We have looked at it very carefully, we have amassed over 400 pages of evidence from around the world.
'Our conclusion, quite clearly, is that "opt out" is not the best way of increasing the number of organs available.'
Spain, for instance, has the best organ donation rate in the world.
"They had presumed consent from 1979 to 1989 and the donation rate was almost flat. Then they made the changes which we are just in the process of beginning and their donation rate is now three times as good as ours.
"We want to see that happen in the UK," said Buggins.
The panel also 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 The law had to be repealed in 1998, principally because of mistrust of government and accusations of body snatching.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. So it is suggesting 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.
Speaking at 10 Downing Street, Mr Brown said: 'I am grateful to the organ donation task force for the work that they have done.
'What they have shown is that a large number of people are willing to give their organs to help other people live.
'They are proposing a plan that would double the number of people in our country who are prepared to donate their organs by volunteering to do so if they die.
'While they are not recommending the introduction of a presumed consent system, as I have done, I am not ruling out a further change in the law.
'We will revisit this when we find out how successful the next stage of the campaign has been.
'The proposal is that we double the number of volunteers to 50%. If we can't get there quickly, then we will return to the proposal I have put forward, which is a presumed consent system'.
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.
Sir Liam Donaldson, UK's chief medical officer, insisted the door must be left 'wide open' to change, despite the review's verdict.
He said: 'People are dying, people are suffering and many people are living on the knife-edge of despair waiting for a phone call that never comes.
'My view has always been that we need to act with solidarity, generosity and humanity to give these people a future.'
Sir Liam argued that advances in transplant medicine, coupled with the ageing population, would mean the demand for organs could only increase.
There are currently almost 8,000 Britons waiting for a transplant. This includes more than 7,000 waiting for kidneys, more than 300 looking for a new liver, 225 in need of lungs and around 100 looking of a new heart.