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Lord Falconer has said it is a 'historic moment' after his assisted dying bill progressed to the next stage following a marathon 10 hours of debate on the issue in the House of Lords.
The approval of the second reading of the Labour peer's proposal has been given the go ahead.
However it must reach a third stage to complete its passage in the Lords, which is likely to happen before Christmas.
If it does not, the House of Commons will have the option to pick up the Bill - although this is not certain.
Even if Lord Falconer's Bill does reach MPs, the looming General Election in May 2015 makes it unlikely the Bill will ever become law in its current form.
A Labour peer whose wife's parents committed joint suicide after his father-in-law was diagnosed with terminal cancer has claimed an assisted dying law could have saved them from a death "clouded by a veil of secrecy and subterfuge."
Lord Mitchell said he had "no hesitation" in supporting Lord Falconer's Bill because it might have spared his family the double bereavement.
Instead of seeking advice, his father-in-law Jack - a Holocaust survivor whose entire family was wiped out by the Nazis - and his wife Ruth cut off communications with their relatives and retreated into a "secret world of preparation and disengagement."
Entrepreneur Lord Mitchell said Jack told him after his diagnosis of acute myeloid leukaemia caused by exposure to radiation: "I'm bloody well going to get out with my boots on." .
"There was not much room for misinterpretation," the peer added.
Former Archbishop of Canterbury Lord Carey has said assisted dying is "compatible with the Christian faith."
He told peers in the House of Lords: "For those who chide me, and they have, that my arguments and my change of heart is light on theological backing, let me tell you what theology is.
"It is about accompanying those very sick and very dying to that place where they feel most abandoned. If that is not theology of the best and purest kind, I really don't know what is."
Conservative peer Baroness Morris of Bolton said she may have used assisted dying laws if they had been around when she broke her back in a riding accident aged just 18.
The Baroness told the House of Lords she became so depressed about never being able to walk again she stockpiled pills as she feared she was becoming a burden to her parents.
She said: "I don't think I would have ever taken them. I just wanted to be free from the pain. But I was lucky. A wonderful nurse befriended me, helped me to feel positive and I got better.
"But what if instead of stockpiling distalgesics, the Bill for assisted suicide and I had been in that frame of mind?"
She said people in Oregon in the US, where assisted dying is legal, had waited up to four days to die after being given a dose of lethal medication and six people had woken up but "none of them had a second go."
Shadow leader of the House of Lords Baroness Royall of Blaisdon said wanting to die was "not a weakness" as the debate on assisted dying continues.
The Labour peer, whose late husband had cancer, said: "For me the goal must be to allow people who are suffering at the end of their life to choose to die.
"This I believe is a matter of compassion and human dignity."
Giving people with terminal illness the right to die would not lead to more deaths, but would mean fewer people suffering "lonely and cruel" ends with the aid of a "plastic bag or a hoard of pills," a Labour peer has claimed.
Former Lord Chancellor Lord Falconer of Thoroton is calling for a "limited and safeguarded" change in the law to allow doctors to prescribe a lethal dose to terminally ill patients judged to have less than six months to live.
Presenting his Assisted Dying Bill in the House of Lords today, he said that while it was important to continue to improve end of life care, for a minority this was not good enough.
He told peers: "The current situation leaves the rich able to go to Switzerland, the majority reliant on amateur assistance, the compassionate treated like criminals."
Professor Stephen Hawking has backed the Assisted Dying Bill that will be debated in the House of Lords today.
The 72-year-old scientist told BBC it was "discrimination against the disabled to deny them the right to kill themselves that able bodied people have."
The Bill proposes allowing doctors to prescribe a lethal dose to terminally ill patients judged to have less than six months to live.
Professor Hawking, has motor neurone disease, said it would be "wrong to despair and commit suicide, unless one is in great pain, but that is a matter of choice."
Peers are set to debate the former Labour Lord Chancellor Lord Falconer's bill today.
The assisted suicide bill was "stacked round with safeguards" to prevent a sick or elderly relatives from being "pushed into death", one campaigner told Good Morning Britain.
Prue Leith, who lost her brother to bone cancer, said she was "not asking for euthanasia" but wanted to give the terminally ill the option of a peaceful death.