A letter, signed by 85 experts from such varied fields as medical, law and ethics, has been published in the Times.
They said the law was outdated and related to an era when "doctors knew best" which was no longer appropriate.
A cross-party group of MPs have tabled a series of amendments to the abortion law, including changing the requirement for two doctors to sign off an agreement for a termination.
The 1967 Act currently requires a woman to prove that carrying on with a pregnancy would be a risk to her mental or physical health.
The tabled amendment would only require a GP to confirm a woman was under 24 weeks pregnant - the legal time-scale in which abortions have to take place.
The lawyers and ethicists who signed the letter back that proposal.
Kent University expert Professor Sally Sheldon, who is one of the signatories, 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.
"Of course, GPs will still have a role to play in abortions. Many women will still want to go to them to get medical information and for a sympathetic ear."
The intervention comes after the British Medical Association called for the end to the two doctor rule at their annual conference last year.
But such suggestions have been bitterly opposed by the anti-abortion lobby.