Women should not have to gain the permission of two doctors to obtain an abortion in Britain, a slim majority of respondents to a survey have said.
Two doctors have to agree to a woman having an abortion
Some 35% said one doctor was enough and 17% said permission should not needed at all, an independent poll carried out for the group Abortion Rights found.
A total of 83% of the 1,000 people polled saw abortion as a woman's right.
This month marks the 40th anniversary of the introduction of the 1967 Abortion Act.
Under the terms of the law, a woman must obtain the permission of two doctors before she is allowed a termination, which can be carried out up until 24 weeks.
The poll, which was carried out over the telephone by the market research group GfK NOP, is said to be the first to ask the public their thoughts on the "two doctor" rule.
The findings mirror those of a Marie Stopes International poll of GPs published earlier this month.
Over half of family doctors questioned said they thought the agreement of just one professional should be enough for an abortion in the first 14 weeks of pregnancy.
Both surveys follow a resolution at last summer's British Medical Association conference calling for abortions to be approved by just one doctor.
"The public clearly feels that the legislation is now out of date," said Anne Quesney, director of Abortion Rights.
"It is time for a law that trusts women to make the abortion decision and remove the need for two doctors' permission to access the procedure - a process that can lead to delays for women at a difficult time."
Broken down into age groups, the figures suggested that the youngest and the oldest have the most reservations about abortion, with 18% of 16 to 24-year-olds and 16% of the those aged 65 and over rejecting the right to a termination.
However, the majority in both groups supported abortion access.
Anti-abortion campaigner Josephine Quintavalle said the figures reflected the public's lack of understanding of what an abortion entailed.
"If there was more information and more discussion of the issues - a greater engagement with abortion - we would see attitudes change and numbers go down.
"The two doctors rule is frequently just a rubber-stamping exercise which no-one should support.
"We need to see doctors taking the time to talk through matters with the woman, not just signing off piles of forms before a patient's name is even written on the top."