The seven Supreme Court justices will rule on a case brought by the Northern Ireland Human Rights Commission (NIHRC), which argues that the current law criminalises "exceptionally vulnerable" women.
The devolved government in the British province is responsible for deciding abortion laws, but Westminster can step in if legislation is deemed to contravene the European Convention on Human Rights (ECHR).
Unlike in mainland Britain, abortion is illegal in Northern Ireland, carrying a potential life sentence, except when a woman's life is at risk or there is a permanent or serious danger to her mental or physical health.
The NIHRC argued in October 2017 that the current law subjects women to "inhuman and degrading" treatment, causing "physical and mental torture" as it bans abortion in cases of rape, incest or serious foetal anomaly.
If the Supreme Court agrees, it will be up to London and Belfast to find a way to bring Northern Ireland into line with the ruling, setting May on a collision course with the anti-abortion Democratic Unionist Party (DUP).
The DUP is the biggest party in Northern Ireland and also props up May's minority government, giving her the votes she needs to get Brexit legislation through the House of Commons.
Adding to the complication, Northern Ireland has been unable to form a power-sharing government for over a year, meaning responsibility may fall on Westminster to unilaterally change national law.
MPs debated the issue on Tuesday, with Labour MP Stella Creasy calling for a nationwide law change.
Northern Ireland minister Karen Bradley insisted that abortion was "a matter for the people of Northern Ireland".
DUP assembly member Jim Wells on Tuesday compared abortion programmes to "the Nazis", highlighting the problems May could have in finding a solution with the party.
The devolved Northern Ireland Assembly voted in February 2016 against legalising abortion in cases of fatal foetal abnormality, rape or incest.
But the case for change has received fresh impetus from the Republic of Ireland's landmark referendum vote to legalise abortion last month.
More than 66 percent of voters backed repealing the constitutional ban on terminations, raising pressure on its neighbour to follow suit.
Sinn Fein and the SDLP, the two major parties representing Northern Ireland's Irish Catholics, and the cross-community Alliance Party, back overturning the ban.
Belfast's High Court ruled in December 2015 that the law was incompatible with article eight of the ECHR -- the right to respect for private and family life -- due to the absence of exceptions in cases of fatal foetal abnormalities and pregnancies resulting from sexual offences.
But three of Northern Ireland's most senior judges overturned that decision in June last year, saying it was a question for the elected assembly, not the courts.
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.ng
![The woman was recorded, among others, while bathing [BI]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'300'%20height%3D'172'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "The woman was recorded, among others, while bathing [BI]")
