The survey of 8,000 members of the medical community found 32.3% supported a change in the law to permit assisted suicide for terminally ill patients.
37.5% said they agreed that 'some change in the law' was needed - compared to 26% who agreed in 2006.
More than 21% said they would "personally participate actively" in helping a patient to end their life - compared with less than 19% eight years ago.
It comes as the House of Lords debates Lord Falconer's bill on Assisted Dying, which would allow those with less than six months to live to end their lives with a fatal dose of medicine.
The Labour peer put forward the private members bill, which had its 2nd reading in July.
Former Archbishop of Canterbury, Lord Carey has come out in favour of the 'Right to Die', but others, including the current Archbishop of Canterbury, Justin Welby, have expressed concern.
He argues changing the law could result in vulnerable, sick patients feeling under pressure to end their lives for fear of being an emotional or financial burden on others.
The Royal College, despite conducting the survey, is officially opposed to assisted suicide, as is the British Medical Association.
The bill is currently still at the committee stage in the House of Lords, with further amendments due to be discussed at a date yet to be scheduled.