"While the government can say that abortion is a devolved issue, human rights are not, and the collapse of the [Northern Ireland] assembly means that the power to right this wrong lies exclusively in Westminster", added Clare Murphy, director of external affairs at the British Pregnancy Advisory Service, a national charity that provides abortion services.
Sarah Wollaston, the Conservative chair of the health select committee in the House of Commons, told the BBC on Sunday that if the Stormont assembly can not get back up and running "at the very least people in Northern Ireland should be allowed a referendum".
Canadian Prime Minister Justin Trudeau also phoned the Taoiseach to congratulate him on the referendum result.
The opposition Labour party called on the government to support legislation to extend abortion rights in Northern Ireland because women are being denied fundamental rights.
And Mr Trudeau tweeted: "What a moment for democracy and women's rights".
Image copyright Reuters Image caption almost two in three Irish voters opted to repeal the Eighth Amendment to the Irish constitution, which effectively banned abortion.
Downing Street insisted it had no plans to offer MPs a vote and that the matter should be left to the Northern Ireland assembly.
"It shows one of the important reasons we need a functioning executive back up and running", a source said.
Since the collapse of a power-sharing administration in Northern Ireland, British officials have been taking major decisions in the region and this means the government could legislate directly despite health being a devolved issue.
"Some of those who wish to circumvent the assembly's role may be doing so simply to avoid its decision".
The current situation "does feel anomalous", she told ITV's Peston on Sunday.
"That hope must be met", she added.
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 United Kingdom".
But Justice Minister Rory Stewart warned against the Commons intervening on the issue.
The prime minister is facing calls from within her cabinet and from opposition parties to scrap the strict rules on abortion in Northern Ireland, bringing the law in the province in line with the rest of the United Kingdom.
Abortions are now only legal in Northern Ireland if the life or mental health of the mother is at risk.
"The settled will of the people has been to afford protections to the unborn life and protect the life of the mother", he said.
Ms Creasy wants to force a vote by tabling an amendment on the upcoming domestic violence bill.
May's government depends on support from the Democratic Unionist Party of Northern Ireland, a deeply conservative party that opposes any attempt to ease restrictions on abortion.
Abortions are only available to women and girls if their life or health is in danger.