A group of academics has called for the two doctor safeguard on abortion to be scrapped in a letter to The Times newspaper.
Under the current law, two doctors must sign a referral form before a woman can go ahead with an abortion.
Pro-life campaigners say that if the requirement is lost, women seeking abortion are more likely to rush into a decision they may regret.
A poll conducted earlier this year showed that most women favour some delay in the process of obtaining abortion.
Nine out of ten women said that those seeking a termination should have a statutory legal right to be warned of the mental and physical health risks associated with abortion before going ahead.
However, one signatory to the letter, law professor Sally Sheldon of Kent University, said: “Medicine is changing.
“It is no longer about the doctor knowing best, rather the emphasis is on the patient being in charge.
“The two doctor requirement has no place in the modern health service and we should not be placing these obstacles in the way of women wanting an abortion.”
An amendment to change the two doctors rule has been tabled to the Human Fertilisation and Embryology Bill, due for its Remaining Stages next week.
It would require a doctor to confirm that a women had not been pregnant beyond the 24 week time limit for abortion, but the second signature would not be required.
The amendment would also remove the requirement to assess the relative risks to the woman’s physical and mental health – creating abortion on demand.
Only one day has been set aside to debate the Remaining Stages of the Bill in the House of Commons.
It is possible that the liberalising abortion amendments may not be voted on.