Eight out of ten of people support a law change to allow doctors to actively end the lives of terminally ill patients who want to die, a poll shows.
Some countries permit assisted dying, but the UK does not
However only 60% supported doctors prescribing, but not administering, drugs someone could use to end their own life.
The British Social Attitudes report surveyed 3,000 people.
Campaigners for a law change welcomed the survey, but opponents said it produced "misleading" results.
Last May, a bill which would allow terminally ill people to be helped to die was blocked by the House of Lords.
Current laws prohibit any form of assisted dying.
WHAT THE TERMS MEAN
Voluntary euthanasia: The physician would actually help the patient die
Physician-assisted dying: A physician prescribes medication which a patient can take to end their own life
In the poll, part of an annual survey by the National Centre for Social Research of people's attitudes to a wide range of subjects, a third said someone with an incurable - but not terminal - illness, such as severe arthritis, should also be able to get help to end their life.
The report says: "The findings suggest that the public does not regard voluntary euthanasia in the black and white terms in which it tends to be regarded by its advocates and opponents."
Only a third thought physician-assisted suicide should be permitted in cases where someone has an incurable illness such as severe arthritis.
And just 44% thought a relative should be permitted to help a terminally ill person die, while only 24% said it should be allowed when someone was not in severe pain or near dying but was completely dependent on carers for all their basic needs.
The report states: "In certain respects the current law that prohibits assisted dying seems to be at odds with public opinion.
"Clear majorities accept that a doctor should be allowed to hasten the death of someone who is painfully and terminally ill.
"On the other hand, only a minority support assisted dying if someone is in pain or dependent, but not terminally ill."
A spokesman for the organisation Dignity in Dying, which supports assisted dying, said: "These findings are in line with almost every other survey in the last 10 years, which consistently show that at least 80% of the public support assisted dying.
"This is just another signal that parliament is out of step with the public on this issue."
But Dr Peter Saunders, campaign director of the Care Not Killing Alliance, said: "This opinion poll, which purports to show that a large majority of people would favour a change in the law to allow euthanasia, is misleading as it has been based on reflex answers to a yes/no question.
"There is no explanatory context about how receiving good palliative care leads people to change their minds about assisted dying, or about how such a law would endanger vulnerable people."
A spokesperson for the British Medical Association said: "We are opposed to euthanasia and physician assisted suicide.
"The BMA has members with wide ranging views on these issues, but at last year's annual meeting the majority of doctors voted to oppose any form of assisted dying.
"We will continue to debate this subject and represent the views of its members."