The British decide: In EU, or out of EU

Millions in U.K. vote on whether to leave the... 02:33

LONDON -- Britons are heading to polls -- many of them wading through puddles and sheltering from their nation's notorious weather to do so -- to vote in a national referendum on whether their country should remain in the European Union.

The vote isn't just about choosing a leader or a government. It's much bigger than that.

CBS News correspondent Mark Phillips says it's about choosing whether Britain remains a part of the biggest, most prosperous trading block in the world, or whether it leaves and risks becoming a less influential little country on the fringes of it.

Why "Brexit" Matters 01:21

It's a vote Prime Minister David Cameron never really wanted to happen. He was forced into calling it by people in the right wing of his Conservative party, who have always wanted to get out of Europe. The referendum promise, made during the last election cycle, was supposed to shut them up. It didn't.

"This Thursday can be our country's independence day," implored Cameron's main rival, former London Mayor and fellow Conservative Boris Johnson on the campaign trail this week. Johnson has led the "Leave" campaign. Much of the campaign, which included a heated battle on the Thames that saw both sides sail up the iconic river in a flotilla, firing cannonballs of rhetorical abuse at each other as they went, has centered on who is telling the biggest lies.

Truth, notes Phillips, has long been flushed down the river here.

How could Brexit impact global economy? 04:14

The "Remain" camp claims British families will be left about $6,000 dollars poorer outside of Europe.

The Leavers say the EU costs Britain about $500 million dollars every week in payments made to the union's headquarters in Brussels, which isn't true.

Aside from the much-muddled economic argument, fear is the greatest component in the campaign; fear that the EU's open border policy will allow a flood of immigrants to overrun Britain.

Nigel Farage, the outspoken leader of Britain's right-leaning UK Independence Party, appeared in front of one "Leave" poster that was later deemed so racist it was withdrawn. The poster shows an image of a long line of refugees streaming out of Syria, with the words "BREAKING POINT" emblazoned across it.

U.K. Inependence Party leader Nigel Farage appears at a campaign stop in front of an anti-European Union poster, part of the "Leave" campaign ahead of Britain's June 23, 2016 referendum on EU membership, that warns of a mass influx of refugees.

In spite of numerous calls for him to do so, Farage has declined to apologize for his smiling photo opportunity in front of the billboard.

Opinion polls showed a virtual dead heat going into the vote on Thursday.

The bookies, however -- often far more reliable than the pollsters -- are predicting a win for the "Remain" camp.

"At one point we thought, to use the horse-racing term, we might need to use photo-finish equipment," Alex Donohue of Ladbrokes bookmakers told CBS News. "Now we're saying there might be a couple of lengths of distance between Remain and Leave at the end."

The smart money, says Donohue, is on the United Kingdom remaining part of the larger union.

Voting stations across the country will close at 10 p.m. (5 p.m. Eastern) on Thursday. The results are expected to come from the official counting office in Manchester on Friday morning.