Both sides have been forced to ramp up their preparations for a disorderly Brexit over the past few weeks.
UK businesses are stockpiling goods while Brussels is trying to find a way to maintain free-flowing operations involving London's massive financial services hub.
- Second referendum -
EU supporters have been calling for another vote ever since the first one backed Leave by a 52-48 margin in June 2016.
There is no law keeping Britain from doing it all over again, but many question whether this would be democratic -- and why a second attempt should take precedence over the first.
It also threatens to be just as divisive with opinion polls showing the country still split over the issue.
Calls for another vote have ramped up over the last few months, with former prime minister Tony Blair on Sunday saying "what seemed a few months ago unlikely is now I would say above a 50 percent likelihood."
Proponents argue that the Brexit people were promised looks nothing like the deal on offer and that Britons never backed a no-deal scenario.
Some members of May's cabinet are reported to be pushing for a second vote, but the prime minister is against the move, warning it "would do irreparable damage to the integrity of our politics."
It is also unclear what options to give people in a second ballot -- and what happens if Brexit wins again.
- Parliament votes on options -
Another possibility that has come to the fore in recent days is for several non-binding votes to be held in parliament on different Brexit options to effectively determine the government's strategy.
The first would be on May's deal but others could include a no-deal Brexit, a second referendum or a "Norway deal" that would keep Britain much more closely anchored to the European single market and allow unfettered immigration.
Business secretary Greg Clark appeared to hint at this on Monday, telling BBC radio that parliament should be "invited to say what it would agree with" if it votes against the draft Brexit agreement on the table.