LONDON -- After 43 years, the U.K. will decide whether to break from the 28-nation European Union on Thursday.

The EU is a "United States of Europe" where people and trade move freely. But conservatives want the U.K. independent.

As political battles go, this one started nasty and then got ugly.

Civility had long flushed down the river by the time the battle of the Thames took place between those who want Britain to leave the European Union and others who want it to stay, reports CBS News' Mark Phillips.

When some Leave EU campaigners unveiled a poster showing imaginary immigrant hoards flooding into Britain, the language got even more poisonous.

A poster showing a mock-up of immigrants flooding into Britain further stirred the Brexit debate. CBS News

"Your campaign hasn't been project fear, it's been project hate," said London Mayor Sadiq Kahn, a campaigner for staying in the EU said during a debate.

Somewhere, among the name-calling, an economic and political argument is taking place. Britain does by far the bulk of it's trade within Europe. And the uncertainty is already hurting, says factory operator Rowan Crozier.

"I've had American customers ask me, prior to placing new business with us in the last two months, 'What do you think's gonna happen?' I don't know, I don't have a crystal ball. I know what I want to happen," said Crozier.

Every major business group wants Britain to stay in, along with every major international financial body and every ally Britain has, including the U.S.

The "Outers" say the EU is holding Britain back with its stifling regulations, its un-elected bureaucracy, and and high costs. The opinion polls say the result is too close to call.

That is, unless you ask the bookies -- who are usually right. The betting money, says Alex Donohue, is going one way in the home stretch.

"At one point we thought, to use the horse-racing term, we might need to use the photo finish equipment. Now we're saying there might be a couple of lengths of distance between 'remain' and 'leave' at the end.

"Staying in the EU is a much stronger bet?" Phillips asked him. "One hundred percent," Donohue said.

Still, the Leave campaign is relying on an emotional, even nostalgic appeal that seems to hark back to the heady days of empire, when nobody told the British what to do.

"If we vote, we can take back control. I believe this Thursday can be our country's Independence Day," said Leave campaigner Boris Johnson.

In the end this is not just about Britain, and not even just about Europe. In a globalized world, destabilizing the EU --- if that's what happens -- shakes up economies everywhere.