Observers say the UK would feel the biggest impacts, positive or negative, from "Brexit," but the EU, too, has much to lose.
Britain's economy is the second-largest in Europe, after Germany. The UK represents 17.6% of the Union's 14.6 trillion euro GDP.
Brexit may not be a "catastrophe," says Charles de Marcilly of the European think tank Robert Schuman Foundation, but it would certainly be an "amputation."
Just under half of Britain's exports go to the EU, and just over half of the country's imports come from the rest of the Union, Marcilly says.
In other words, Britain's economy is closely integrated with the rest of Europe.
Right now, that trade benefits from the free trade zone that's central to the EU. Now the UK's decided to leave, that would all be subject to re-negotiation.
The UK is an important diplomatic player that has long prided itself on "punching above its weight."
In a field where symbolism is incredibly important, Britain boasts nuclear-weapons capability and a permanent seat on the U.N. Security Council.
"EU foreign policy is not exactly a great success story," says Jan Techau of Carnegie Europe
. But "whenever the EU has done something useful and forceful" -- such as sanctioning Russia over the war in Ukraine or negotiating with Iran -- "Britain played a crucial role in that."
"Without Britain as part of the mix, not only do we lose one of the countries that has a naturally global outlook," says Techau, "but also one of the real diplomatic heavyweights within the EU -- big foreign service, traditionally strong abroad, a potent military power in the European context as well."
London has 123 embassies around the world. Its history as a colonial superpower means association with 52 other members of the Commonwealth.
The British military stands out in the European Union for its size and capability. Within NATO, only the United States spends more on its military.
And the UK also stands out for its willingness to use military power abroad. While Germany is widely seen as the EU's leader, economically and politically, its history means it is very reticent to exercise that power by force abroad.
"An EU without Britain will certainly be a less potent and a less powerful player, and that's not a good thing," explains Techau.
Right now, says Techau, there is a relative balance within the EU "between a more state-centric economic vision versus a more free-trading capitalist model."
The UK "stands for an open-market, capitalist system; a single market; free trade.
"All of those good things that have made the EU bigger and greater and a better organization will be damaged by...Brexit."
Doru Frantescu of the Brussels-based NGO Vote Watch Europe
"The leftist forces -- those who favor more integration, harmonization of taxation across the EU -- have tried for years to ... impose EU regulation on how and what should be taxed in the member states.
"This has not happened also because of the position of the UK representatives in the Council and in the European Parliament.
"But with the British representatives out of these bodies, there will be a momentum for those who propose more red tape, more taxation, to promote their agenda on these policies."
Perhaps it's obvious, but Britain's membership in the Union promotes, well, union.
"If one of the key members of the club leaves the club," says Frantescu. "Automatically the other ones will think 'is this club still worth being in?'"
"It will look very bad to the outside world that an important country like Britain deems this club so ludicrously bad that it wants to leave," says Techau.