Members of parliament have submitted amendments calling for the limit to be reduced to as low as 12 weeks, although many of those supporting a change are expected to rally round a proposed cut to 20 weeks.
The government does not support any alteration to the current legislation on abortion, but has allowed the amendments as part of the debate on its Human Fertilisation and Embryology Bill. MPs have been given a free vote on the issue, as is traditional on abortion matters.
Conservative leader David Cameron has said he will vote for a reduction to 20 weeks, while Prime Minister Gordon Brown says he will vote against any change.
Some anti-abortion campaigners say the law should be amended because advances in medical science mean some babies born before 24 weeks are able to survive.
But those who favour the status quo cite recent medical evidence from the University of Leicester showing there has been no improvement in survival rate over more than a decade.
Around 200,000 abortions were carried out in Britain in 2006, of which about 3,000 were conducted after 20 weeks.
The abortion limit was reduced to 24 weeks from 28 weeks in 1990.
MPs also have a free vote on a proposal in the bill to remove the requirement for doctors to "consider the need for a father" when offering fertility treatment, seen as making it easier for lesbian couples to obtain in-vitro fertilisation (IVF) treatment.
Religious groups have condemned the measure as anti-family and some MPs have submitted an amendment against it.
On Monday parliament defeated an amendment to ban inter-species research - in which human DNA is injected into cells derived from animals - by 336 to 176 after hours of impassioned debate on ethics versus science.
In a separate vote, MPs also decided to allow parents of children suffering serious diseases to use IVF to select "saviour siblings" who can act as donors for transplants to save their sick brothers and sisters.
