While both May's Conservatives and the opposition Labour Party now explicitly support leaving the club the United Kingdom joined in 1973, some of the Union's most powerful politicians have raised the possibility of Britain cancelling Brexit.
Will Brexit actually happen? And if it does, how might it look? Following are some of the options.
1) BREXIT IN NAME ONLY
Under this scenario, Britain leaves the EU but gets a deal that is as close as possible to EU membership.
Before the June 8 election, May proposed a clean break from the EU: leaving its single market, which enshrines free movement of people, goods, services and capital, and proposing limits on immigration and a bespoke customs deal with the EU.
But the election result deprived her Conservative Party of its majority in parliament, and such is the collapse of May's authority that her Brexit strategy is being picked apart - and softened - in public by her ministers, lawmakers and allies.
"When the British people voted (in the EU referendum) last June, they did not vote to become poorer, or less secure," British finance minister Philip Hammond said in a speech this month.
"They did vote to leave the EU. And we will leave the EU. But it must be done in a way that works for Britain," Hammond said, adding that he wanted an agreement for trade in goods and services and a transition deal to avoid unnecessary disruption.
The Brexit referendum result, under this scenario, would be formally honoured but Britain would remain either in - or very close - to the single market and the customs union and with some deal on immigration, while paying membership dues to the EU.
London Mayor Sadiq Khan has called for continued membership of the single market, though it is unclear what the EU would demand for such a deal.
One option would be a long transitional arrangement that would preserve a British quasi-membership for years to come. Or the negotiations could be extended beyond the expected leaving date of March 2019.
Immigration would be the hardest riddle to solve: Big businesses want cheap labour but many British voters see leaving the EU as a way to stop the unlimited immigration from the bloc that membership of the single market implies.
For Brexiteers, an EU exit that left Britain so close to the bloc - and so subject to EU regulation - would be a sellout.
2) BREXIT NEVER
Brexit doesn't happen: The $2.5 trillion economy stalls, prompting calls for a second EU referendum that - if held during a deep recession - could produce a vote to remain in the EU.
"Many are secretly and shockingly praying for a recession: they want people weeping in the streets from economic pain so that they can have a second EU referendum," said Richard Tice, who helped found one of the two Leave campaign groups.
"If that happened all bets would be off and we would be in a democratic and constitutional crisis in Britain the likes of which none of us have ever seen in our lifetimes."
If the Brexit decision was reversed by a second vote, the Article 50 notice that triggered formal divorce talks would be withdrawn, though there is no legal certainty on how, and Britain would remain a member of the EU.
Other routes to a Brexit halt include disrupting the British government's exit legislation, battling Brexit in the courts or the rise of a credible pro-EU politician who could challenge the consensus and the leaderships of both major political parties.
French President Emmanuel Macron has said the EU's door remains open, and German Finance Minister Wolfgang Schaeuble has also indicated Britain could be welcomed back.
European Council President Donald Tusk even invoked the lyrics of John Lennon to imagine a Brexit rescinded.
Many opponents of Brexit - the "Remainers" - would rejoice, though a reluctant and divided member of the EU could hinder European attempts at further integration.
"If all went well, the two parties may want to remarry even before they have divorced," said billionaire investor George Soros.
Cancelling Brexit or holding a second EU referendum would trigger a major crisis in Britain with uncertain consequences.
"The election result is certainly a bump in the road for Brexiteers, but its significance should not be overplayed," said Matthew Elliott, who was chief executive of Vote Leave, the official leave campaign in last year's referendum.
"Recalcitrant Remain supporters are understandably buoyant but, as with their Article 50 hopes, their optimism will be shown to be misplaced."
May has been clear Brexit will happen.
3) DISORDERLY BREXIT
With her authority so weakened, May will have to gauge whether she can get a deal from the EU that she can sell at home.
If she thinks she will fail to get a Brexit deal through parliament, some business leaders fear she will allow talks with the EU to collapse and take Britain out with no deal.
A disorderly Brexit could spook financial markets, tarnish London's reputation as one of the world's top two financial centres and sow chaos through the economies of Britain and the EU by dislocating trading relationships.
May repeatedly said during the election campaign that "no deal is better than a bad deal", though she has been less forthright since the election result.
A crisis in the EU or euro zone could persuade Britain to walk out without an agreement.
4) A THERESA MAY BREXIT
Theresa May has proposed a clean break from the European Union, making control over immigration and ending the jurisdiction of the European Court of Justice the priorities.
She has said that this entails leaving the single market and customs union, but that she wants a trade deal to secure the best possible access to the bloc.
May has said she will work with lawmakers, businesses and the devolved administrations in Scotland, Northern Ireland and Wales to reach a consensus on Brexit.
On Thursday she set out what she called a "fair deal" for EU citizens living in Britain, saying in her first test of negotiating strength that she did not want anyone to have to leave because of Brexit or to split up families.
But many observers believe May will no longer be prime minister when Britain leaves the EU. - Reuters