Thousands of women could be banned from having an abortion under plans being drawn up by anti-abortion groups.
Babies with genetic disorders can be aborted in the UK
They are hoping to use the new European Union constitution to stop women from aborting babies with severe genetic disorders, like Down's syndrome.
They claim aborting these babies is akin to "eugenic practices", which is outlawed under the EU's Charter of Fundamental Rights.
The charter will apply to the UK when the constitution comes into force.
It requires "the prohibition of eugenic practices, in particular those aiming at the selection of persons".
The UK government is committed to signing the European constitution.
Anti-abortion groups believe they can use the charter to tighten up the rules on abortion.
Any such challenge would have to be made through the European Court of Justice.
Professor Jack Scarisbrick, national director of the charity Life, said he was confident they could win.
"If you have a law which says special needs children can be killed, you are clearly practising eugenics," he told BBC News Online. "It is weeding out substandard human beings."
The Pro Life Alliance said it was seeking legal advice on the issue.
"It is very early days, but we have asked for a legal opinion on it," its spokeswoman Josephine Quintavalle told BBC News Online.
"We are looking at whether the charter will give that sort of path of challenge. From what we have been told, the clause in the charter is unalterable."
However, a spokesman for the Foreign Office suggested they did not have a case.
"The article they are referring to will prohibit eugenics," he told BBC News Online.
"But in the explanatory guide which follows the article and which is supposed to be taken into account by the European judges it says that this refers to selection programmes.
"This includes campaigns for sterilisation, forced pregnancies, compulsory ethnic marriage and all acts deemed to be international crimes in the statute of the international criminal court.
"The idea is not to restrict the individual or the individual's choice but rather to protect the individual."
Professor Piet Eeckhout, director of the Centre of European Law at King's College London, also raised doubts over whether there was a case.
"There is quite a lot of misunderstanding about this charter," he said.
"It is primarily a charter that binds EU institutions and member states at a national level. It applies to EU laws. As there is no EU law on abortion the charter would not apply in this case."
The pro-choice British Pregnancy Advisory Service described the move as ridiculous.
"They are on a hiding to nothing," said Ann Furedi, its chief executive.
"Abortion is permitted on the grounds of foetal abnormality in Britain. But that is not to say it represents any form of eugenics.
"Eugenics is about trying eliminate certain types of people or characteristics from the population. It's a social movement.
"When women take the decision to end a pregnancy affected by Down's syndrome or spina bifida they are making a personal or individual choice.
"It would be ridiculous for anyone to suggest woman making that decision is doing so with any eugenic intent."