The "overwhelming majority" of the public supports the Assisted Dying Bill, a group of experts has said in an open letter urging parliament to pass the right to die law.
Signed by 80 doctors, clerics, actors, writers and politicians, the letter – given to the Daily Telegraph – says the government must commit to changing the current euthanasia laws.
Put forward by Lord Falconer, the former Lord Chancellor, the Assisted Dying Bill would make it legal for people to choose to end their lives.
Doctors would be able to prescribe a fatal dose of drugs to terminally ill people as long as they had less than six months to live and had shown a "clear and settled intention" to end their own lives.
Signatories claim that at present, one person from Britain visits the Dignitas clinic in Switzerland to die every two weeks. For every person going abroad, they add, 10 more people take their own lives at home.
"The overwhelming majority of the public supports law change on assisted dying and no one believes that someone should face a prison sentence of 14 years for compassionately assisting a loved one to die," the letter said.
"We are closer than ever to allowing dying people to have safeguarded choice in how they approach their deaths. Whoever forms the next Government must allow time for parliament to reach consensus on a safeguarded law."
Signatories include the former Archbishop of Canterbury Lord Carey, Booker Prize winning author Ian McEwan and Sir Chris Woodhead, the former chief inspector of schools. Other supporters include Sir Patrick Stewart, Jo Brand, Eric Idle and Hugh Grant.
David Cameron has previously said he would be opposed to any law that would legalise suicide, but said MPs would be given the opportunity to vote if it was debated in parliament.
Currently, assisted suicide carries a sentence of up to 14 years in prison. Opponents claim the law could make vulnerable people feel pressured into taking their own lives.
The bill would not pass before the forthcoming general election and signatories say the next government must push ahead with the discussion.
"If there is not enough time for the (Lord Falconer's) Bill to complete its stages before the general election then it is imperative that Parliament continues this important debate afterwards," the letter said.