Ministers – including within her own Cabinet – have indicated their support for liberalisation of laws to resolve an “anomaly” within the British Isles.
Scores of MPs across the House of Commons have indicated they are prepared to act to rewrite the current legislation given the absence of a devolved administration in Stormont.
But the Prime Minister faces a political headache over calls to act because her fragile administration depends on the support of the ten Democratic Unionist Party MPs – who strongly oppose any reform to Northern Ireland’s strict laws.
And Westminster intervening in a devolved issue could also lead to wider concerns about the political situation in Northern Ireland.
In a post on Twitter, Mrs May said: “The Irish Referendum yesterday was an impressive show of democracy which delivered a clear and unambiguous result.
“I congratulate the Irish people on their decision and all of #Together4Yes on their successful campaign.”
Downing Street is understood to believe that any reform in Northern Ireland “is an issue for Northern Ireland”.
“It shows one of the important reasons we need a functioning executive back up and running,” a source said.
But in a sign of the pressure from within Mrs May’s own party, Education Minister Anne Milton suggested she would back liberalisation if there was a free vote.
The current situation “does feel anomalous”, she told ITV’s Peston on Sunday. Cabinet minister Penny Mordaunt – who is responsible for the women and equalities brief in government – said the referendum signalled a “historic and great day for Ireland” and a “hopeful one for Northern Ireland”.
Former women and equalities minister Justine Greening said: “It’s clear it’s now time for debate and action to achieve the rights for NI women that we have as women across the rest of the UK.”
But Justice Minister Rory Stewart warned against the House of Commons intervening on the issue.
He told BBC’s Sunday Politics the UK government was acting as a “caretaker” administration in the absence of Stormont, and “that must not be used to make fundamental constitutional, ethical changes on behalf of the people in Northern Ireland”.