JUDY WOODRUFF: The United Kingdom has been a part of the European Union for more than 40 years. But its place in that postwar attempt at European integration is now in question, and whether Britain will stay or go is a hotly-contested issue that will soon go before British voters.

DAVID CAMERON, Prime Minister, United Kingdom: I have no other agenda than what is best for our country.

JUDY WOODRUFF: It was a high-stakes moment, the British leader appealing to the House of Commons, and to the country at large, not to bolt from the European Union.

DAVID CAMERON: Our current trade agreements with 53 countries around the world would lapse. This cannot be described as anything other than risk, uncertainty, and a leap in the dark that could hurt working people in our country for years to come.

JUDY WOODRUFF: David Cameron said the deal he struck with 27 other E.U. nations on Friday grants Britain special status. It includes measures to ensure Britain won't be forced into becoming part of a European super-state. It also creates safeguards for Britain's financial services and the pound currency. And it grants London the power to limit welfare payments to migrants from the rest of Europe.

Cameron is depending on that deal to win over doubters in his own Conservative Party. But the effort was dealt a major blow yesterday when London's popular mayor and fellow Conservative Boris Johnson came out in favor of leaving the E.U., what's become known as the Brexit.

MAYOR BORIS JOHNSON, London: I will be advocating vote leave or whatever the team is called. And I understand there are many of them. I think that is basically — because I want a better deal for the people of this country, to save them money and to take back control.

JUDY WOODRUFF: Johnson's announcement could increase the odds that Britons will vote to leave the E.U. in a June referendum. But opinions were decidedly mixed on the streets of London.

BECKY, London Resident: We'd be just better off on our own. I think, you know, we have been an island for a long time, and I don't think we need to rely on other people.

ANDREW, North Yorkshire Government Official: Europe protects our employment rights, our human rights and maybe they keep our government in control.

JUDY WOODRUFF: Leaders of other E.U. member nations, including Italian Prime Minister Matteo Renzi, also criticized a possible exit.

MATTEO RENZI, Prime Minister, Italy (through interpreter): The consequences would be worse for British citizens than for European ones. We hope this will not happen, but were I to make a forecast, if Great Britain leaves, the main problem will be for the U.K., its businesses and its citizens.

JUDY WOODRUFF: The uncertainty over Britain's future in the bloc has already taken a toll. The British pound's value fell more than 2 percent today.

With me now to discuss the political battle of Britain's possible exit from the European Union and its implications is Steven Erlanger. He's the London bureau chief for The New York Times.

Steve Erlanger, thank you for joining us.

Why, after decades of being part of the E.U., are so many Britons looking to leave it?

STEVEN ERLANGER, The New York Times: Well, we still don't know how many are really looking to leave it. Certainly, there's a big portion of the Conservative Party which has wanted to leave it probably ever since Britain joined it.

In 1975, 41 years ago, there was a similar referendum which passed by, like, two-thirds to one-third to join it. But ever since Margaret Thatcher demanded her money back, John Major had lots of trouble with the Conservative Party angry about Brussels, angry about what they perceived to be loss of sovereignty.

And to manage his own party, David Cameron thought he should promise them this referendum, this in-or-out referendum on Brussels, if he won power again. Well, lo and behold, even to his surprise, he won a majority, so he sort of caught himself and felt that he had to make good on his promise and hold this in-or-out referendum.

JUDY WOODRUFF: So what are the main arguments today for leaving the E.U.?

STEVEN ERLANGER: Well, some of them are historical and nostalgic. Britain is an island that was an empire. It's never been fully European, but it's too close to Europe to escape it, too.

It was very much engaged in the great European wars, but it won them, and so it has a different sense of its own sovereignty than, let's say, France or Germany, or Belgium, which understand that sovereignty can be vulnerable.

And Britain isn't — it's an Anglo-Saxon country. It has a different notion of laws. It's not the Napoleonic code. So that's one thing. And the second thing is the British sense of sovereignty. They feel Parliament really must be sovereign, and the people who want to leave feel Brussels interferes too much in the operations of British laws and British justice.

And the third major issue, which is an odd one, really, is immigration, because when you're part of the E.U., you have to guarantee freedom of movement and freedom of working for every citizen of the E.U. So they're worried about their jobs.

JUDY WOODRUFF: So, quickly, what are the main arguments in the other direction that Britain should stay in, and who's making them?

STEVEN ERLANGER: Well, the main lessons are, Britain is part of Europe, it's inescapable, even the wars show that.

Britain's security is guaranteed by being part of this larger group. Britain's trade is heavily toward the European Union. At least a million Britons also take advantage of this freedom of movement and freedom of labor and live inside Europe. And the city of London, which is a big financial center, benefits more from being inside the E.U. than not.

There are a lot of companies who are based in Britain because they want to be part of the E.U., but also favor British labor laws. So, if Britain leaves, the great worry is some of those companies will leave, that there will be capital flight, that Britain's security will be diminished. And, also, the Americans have been very clear about wanting Britain to stay in.

JUDY WOODRUFF: And that's exactly what I wanted to pick up on. What is it felt is the U.S.' stake in all this?

STEVEN ERLANGER: Well, the U.S. is not being altruistic.

The U.S. sees Britain as a great ally, and it wants its great ally inside the European Union, which has a big effect, frankly, on global trade regulations, on data privacy regulations. And the U.S. feels, with its ally Britain, it has more influence inside the European Union than it would otherwise.

And, also, Britain is a big military power with France, and it's good to have Britain not just inside NATO, but inside the European Union itself.

JUDY WOODRUFF: So, I guess you're looking for a lively debate for the next four months.

STEVEN ERLANGER: Well, it's going to be lively, partly because what's added spice is, now the Conservative leadership is at stake, because Boris Johnson, the mayor of London, who's always considered slightly buffoonish, but also very popular and a possible prime minister, has broken with David Cameron, and is favoring exit, while Cameron wants to stay inside.

And Cameron's quite angry with Johnson, but Johnson, I think, sees it as his best chance of becoming prime minister down the road.

JUDY WOODRUFF: Drama at every level.

Steven Erlanger with The New York Times, we thank you.

STEVEN ERLANGER: Thank you.