Hundreds of lives could be saved each year under a new opt-out system for organ donation.
Under the plans adults will be presumed to be organ donors unless they have specifically recorded their decision not to be.
The Government has estimated that such a scheme would save up to 700 lives each year.
The measures, put forward in the Organ Donation (Deemed Consent) Bill, follow on from a high profile campaign by 10-year-old Max Johnson, who was saved by a heart transplant and subsequently demanded a change in the law.
Labour MP Dan Jarvis, who spoke in support of the Private Members’ Bill, said: “This is a Bill which will save lives, but it is important to note that of all the people who died in the UK last year only about 1% died in circumstances that would have made a donation possible.
“This means that even though hundreds of thousands of people across the country are registered as potential donors, only a small handful will ever be in a situation that would allow a donation to take place.
“This is one of the main reasons why today in the UK there are thousands of people waiting for an organ donation and why every year hundreds of people will die waiting.
“This loss of life is devastating but it is not inevitable.”
He added: “I believe that moving to an opt-out system for organ donation, like the one they have in Wales, will add thousands of names to the donor register, meaning that once the Bill is passed hundreds of lives could be saved.
“This is not about the state taking control of people’s organs or shaming people into donating. If people do want to opt-out that is absolutely fine and I am entirely respectful of any decision of any one for whatever reason so to do, no questions will be asked and there will be no hard feelings.”
If passed, the measures are expected to come into effect in England in spring 2020 – because the timetable for its introduction will allow for a year of “transition” to the new law.
The Government has said it would also encourage people to discuss, with their families, the issue of whether they would want to be a donor in the event of their death.