THE debate about British membership of the European Union has reminded me of the 1990s, when Rudy Giuliani used to say that he was happy to have the United Nations headquartered in Manhattan because it bolstered his boast that New York City was the capital of the world. Although it pains me as a New Yorker to say this, 20 years on, it is London that has a far more compelling claim to that unofficial status. Unless, that is, British voters snatch it away in the referendum on EU membership on June 23rd.

London has changed utterly in the two decades since Mr Giuliani‘s comment. Although always charming, the British capital back then was not known for its clean air, variety of cuisine, efficient public transport or the tranquility of its workers. It was capital of the United Kingdom, yes, but it was no mecca for Europeans.

Today, London is more important, and more hospitable. It is a magnet for people from every corner of Europe and beyond, and not just political exiles and globe-trotting billionaires. Businessmen, bankers, entrepreneurs, and waiters and builders, too, all come here by choice. Even the miserable weather does not deter them.

Globalisation and the communications revolution have locked in English as the world’s first language, and language matters in international diplomacy. When the great powers meet, the British foreign office often does the drafting, because of centuries of diplomatic experience and the fact that the text is always in English. And language is just one of many reasons that British theatre, films and music are so popular all over the world. A friend of mine spends half his life on planes to Asia arranging the export of musicals created in London to cities all over China and India.

London is still Europe’s financial capital. But it is also the global centre for other specialised service professions, like lawyers, accountants, public-relations experts, and business consultants. Most of the top firms in these fields may serve countries all over Europe, but they are based in London. If Britain were out of the EU, international companies might no longer be able to use London as a hub for all their European operations.

Brexit would mean practical and psychological changes, too, as the free movement of people ends and lengthy negotiations on immigration and travel begin. All those Europeans who have found it comfortable and easy to live and work in London will discover it is a lot harder when the British are no longer EU members.

There is no doubt that the Iraq disaster and the EU debate have affected Britain’s international clout. The days of Ronald Reagan and Margaret Thatcher are long gone. If Britain decides to leave the EU, I can imagine White House aides saying a presidential trip to Europe does not require a stop in London.

But for now, at least, London allows for one-stop shopping. Britain is still a central player in every major international organisation. It is one of five permanent members of the UN, and one way or another sits at the top table in NATO, the international financial institutions, and the Commonwealth. At the same time, the EU still retains its significance, even amid its problems. Whether it is imposing sanctions, removing sanctions, threatening sanctions, denouncing some international development, or setting the diplomatic predicate for stronger steps, including the use of military power, the EU is a critical global player.

As a result, Britain is now unique, for its diplomats are plugged in to all the key levers available in the international system. Why throw that away?

Politically, the price of payback will be far higher than “leave” campaigners admit. They argue that the EU needs the British so much that they will forget all that has happened this year. But having watched international diplomacy as both a participant and an observer for 25 years, I doubt the leaders of most European countries will assign a high priority to negotiating a new arrangement with Britain. Scheduling meetings with EU officials will be hard enough, never mind striking compromises to satisfy British officials. Contrary to the claims of some “leave” advocates, negotiating trade arrangements and regulations and immigration, among others, will be nasty, brutish and long.

Young and middle-aged Europeans are attracted to London. They come because they want to. If the British leave the EU, those days will be gone, and so will the label “capital of the world”. Neither will come back.

James P. Rubin was assistant secretary of state for public affairs during the Clinton administration. He is currently the chairman, with Robert Kagan, of a study group on "extending American power" for the Centre for a New American Security