As the European Union prepares to put a squeeze on the U.K. and everyone else tries to wade through a Brexit's ultimate consequences, there is the looming possibility that it may not happen at all.

The referendum was not legally binding, and no EU member state can force the U.K. to initiate Article 50 of the Lisbon Treaty — the critical first step to formally initiate the divorce.

Once notice of Article 50 is given, there's a two-year window to negotiate the terms of the U.K.'s exit.

James Strong, a fellow in foreign policy and international relations at the London School of Economics, estimates the multitude of other deals the U.K. will need to work out individually with the 27 remaining EU members will take anywhere between five and 10 years, assuming deals are reached at all.

So how could the U.K. potentially walk away from its plan to, well, walk away from the EU?

There's no doubt the options are dwindling by the day. Key European leaders, like German Chancellor Angela Merkel, have said publicly that there's no turning back on a Brexit. Even British Prime Minister David Cameron said he considered the referendum binding.

But Cameron will be replaced by September, and until Article 50 is invoked, there are ways to abandon a Brexit. At least in theory, that is.

Move along, nothing to see here

The British government could simply ignore the referendum result. The vast majority of sitting MPs are firmly in the Remain camp, so there could be enough political will to wait out the storm.

In reality, though, that would amount to ignoring 17.4 million Britons who voted Leave and would only deepen the anti-establishment populist anger that fuelled at least a portion of those voters in the first place.

"It would be the political elite turning around and saying, 'We're simply going to ignore the wishes of the people'," says Nicholas Wright, a teaching fellow in EU politics at University College London, adding that he believes "it's extremely unlikely" that the U.K. won't move forward with Brexit.

"There's going to be a lot of angry people if clever politicians don't follow through on their promises."

German Chancellor Angela Merkel has said there's no need to rush into triggering Article 50, but she's also been firm in her conviction that a Brexit is inevitable and must eventually proceed. (Hannibal Hanschke/Reuters)

That being said, more than 16 million Britons cast a ballot to remain in the EU. Even former London mayor Boris Johnson, one of the most prominent Leave campaigners, admitted in a meandering op-ed that the referendum result was "not entirely overwhelming."

Another referendum?

There have already been calls for a second referendum, among them an online petition with more than four million signatures as of Wednesday afternoon.

There are two ways this could go down. The first is to have another vote right away. But it's a route fraught with obstacles, least among them poor optics.

"One of the big drivers of Leave sentiment has been a sense among economically disadvantaged voters that their voices were not being listened to," says Strong.

Former London mayor and Leave campaigner Boris Johnson has had a tough week. He told reporters that a convoluted editorial he penned outlining what a Brexit will look like was hastily put together and that he should have slept more before writing it. (Stefan Rousseau/Reuters)

"To ask them to think again on the same question would only compound that sense."

Alternatively, the U.K. could try to hold off on triggering Article 50 while it negotiates more satisfactory terms with the EU, then take the new deal to a referendum. There's speculation, Strong says, that this was the endgame that some of the more moderate Leave supporters always intended.

After Cameron's trip to Brussels to meet with other EU leaders this week, however, this seems a very unlikely outcome.

European Commission President Jean-Claude Juncker was outright hostile, and the European Parliament passed a motion calling on the U.K. to invoke Article 50 as soon as possible.

'Well I have to say, you're not laughing now, are you?' 1:54

Other EU members need to see an end to the uncertainty of if, or when, the U.K. will formally initiate the divorce process, and they'll do what's necessary to ensure that, says Strong.

"This might be a good time for Britain to be as co-operative as possible," he adds.

New government, clear mandate

Alternatively, there are some who argue that the gravity of the situation necessitates a general election. That way U.K. voters could elect a government that campaigned on a clear mandate, whether it's Leave or Remain.

But both major parties are awash in the political chaos unleashed by the Brexit vote.

Labour Leader Jeremy Corbyn is facing a full-scale revolt within his party. The mutiny has essentially left Britain without a united, functioning opposition in the House of Commons. (Christopher Furlong/Getty)

Labour leader and notably tepid Remain supporter Jeremy Corbyn is facing mutiny. This week 48 Labour MPs resigned their shadow-cabinet posts in protest of Corbyn's leadership, and on Tuesday he lost a non-confidence vote 172-40. He refuses to step aside.

For their part the Tories need to find a new leader, and it's clear that, just like in Labour, deep schisms have opened in the party.

Strong also points out that it's not clear what would happen if a new government, elected on a promise to keep the U.K. in the EU, came to power after Article 50 is triggered. Could it reverse course on Brexit? Maybe, maybe not, he says, as the EU's governing treaties are vague and, at best, open to interpretation.

The Scottish question

Lastly, there is a question of whether Scotland, which voted overwhelmingly Remain, could veto legislation marking the U.K.'s split from the EU. An April report by the British House of Lords concluded that approval would have to come from Scotland, Northern Ireland and Wales.

According to a Vox.com report, however, the British Parliament could simply repeal that law if it was intent on a Brexit.

Scotland's First Minister Nicola Sturgeon has already signalled that in the case of a Brexit her country will seek a second independence referendum, possibly opening the door for Scotland to join the EU on its own.

No matter what plays out in the coming months, the political turmoil will only continue, Strong says.

"There's simply no plausible outcome of the process going forward that a majority of the British public will support."