Conservative MP Heidi Allen gave an emotional speech to the chamber
However, a different four of the seven ruled that the Northern Ireland Human Rights Commission, which had initiated legal proceedings to try to liberalize the law, did not have the right to bring the case.
But, by a majority ruling, the judges expressed the "clear opinion" that the current legislation is "incompatible" with European human rights laws in the cases of fatal foetal abnormality, rape and incest.
"A majority of the court does however consider that the current law in Northern Ireland is disproportionate and incompatible with Art 8 ECHR insofar as that law prohibits abortion in cases of (a) fatal foetal abnormality, (b) pregnancy as a result of rape and (c) pregnancy as a result of incest".
Sarah Ewart, a Northern Ireland woman who was forced to travel to the United Kingdom for an abortion after being told her baby would not survive said getting involved in the case had been worth all the effort.
But even though the judges formally rejected the appeal before them, the legal opinions accompanying that rejection have spurred pro-choice campaigners to say that the Westminster government must act to effectively overrule devolution in Northern Ireland, and impose reform direct from London.
Submissions were made at the Supreme Court by a number of bodies, including seven of the UK's leading reproductive rights organisations, Humanists UK, Bishops of the Roman Catholic Dioceses in Northern Ireland, the Society for the Protection of Unborn Children and Amnesty International.
Human rights group did not have standing to make appeal, court rules.
She added: "It is a matter of fundamental human rights on which, hard though it is, the courts are as well qualified to judge as is the legislature".
However, a majority of justices also found that the Northern Ireland Human Rights Commission, which had initiated legal proceedings to try and liberalise the law, did not have the powers to bring the case.
"This is hugely significant and makes clear there is nowhere left for the government to hide on this issue".
The decision comes after the Republic of Ireland voted to repeal its Eighth Amendment, legalising abortion for Irish women up to 12 weeks after conception "with no restriction as to reason".
"All eyes are now on the UK Government", Teggart added.
The maximum penalty for breaking the law in Northern Ireland is life in prison. "A failure to act would be a cruel betrayal of women".
"No formal declaration has been made by the court and the appeal has been dismissed, but the analysis and comments from the court on the issue of incompatibility will be clearly heard by the House of Commons and politicians in Northern Ireland".
Northern Ireland's elected assembly, which has powers to legislate on the issue, voted against liberalising the law in February 2016.
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