Dame Esther, who has been calling for a change in the law, said she was surprised she may live to see a debate in Parliament about the issue.
She said the law as it stands puts her family “at risk of being accused of killing me” if they helped her end her life in Switzerland.
“All I’m asking for is that we be given the dignity of choice,” Dame Esther told the BBC.
“If I decide that my own life is not worth living, please may I ask for help to die. It’s a choice.”
But Dr Lucy Thomas, a palliative care and public health doctor, said assisted dying was a last resort that courts, rather than doctors, were better placed to judge.
She added that choosing to end your life was not a “straightforward consumer decision”.
Baroness Grey-Thompson told the BBC she was opposed over concerns “about the impact on vulnerable people, on disabled people, coercive control, and the ability of doctors to make a six-month diagnosis”.
Assisted suicide – intentionally helping another person to end their life – is currently banned in England, Wales and Northern Ireland, with a maximum prison sentence of 14 years.
Assisted dying is generally used to describe a situation where someone who is terminally ill seeks medical help to obtain lethal drugs which they administer themselves.
As a backbench MP, Leadbeater would not normally be allotted time for a full debate and vote in Parliament on one of her proposed bills.
However, earlier this year she came first in the private members’ ballot, meaning she will be given some of the limited time available for backbench MPs’ bills.
Speaking to the BBC, the Spen Valley MP said topping the ballot had prompted her to look into the subject of assisted dying “in a lot more detail” and that she believed there was a “real appetite” for MPs to have a debate.
“The current situation isn’t particularly safe and there isn’t actually the choice that I believe people deserve and should have,” she said.
