Since the 1980s, the bodies that award great global events such as Olympics Games, World Cups, and Expos to cities have changed their approach. Rather than see host cities and nations go bust trying to present such events, they now focus on “legacy”—the accumulated benefits that accrue to the hosts. These are carefully conceived and defined, planned and managed, and notionally set against the considerable costs of hosting to produce a positive number.

But legacy is a tricky concept. The way that infrastructure, urban development, business investment, tourism, identity, social improvements, and better coordinated city management are produced is shaped by local processes and institutions. These benefits accumulate over different time frames, some requiring several decades to emerge and some coming in advance of the event—not so much as a legacy as an early dividend. They also are realized within different geographies, some focused on the hosting locations and districts, others spread over a wider region or the entire nation.

Some benefits are direct outcomes of the event, such as new facilities, infrastructure, and amenities, and tourist spending during the event. Others are more indirect, such as property-market improvements or an enhanced identity and image for the host city. Other supposed legacies could more accurately be considered associated benefits that may emerge as a result of other activities—not an outcome of the event, but perhaps something encouraged by it, such as improved health or skills of local people, a reduction in crime, or increased business investment or exports. These activities are potentially connected to hosting the event, but they are not a legacy in any meaningful way.

London has already done a great job getting ready for the Olympic Games. The facilities and infrastructure are all ready, and many have future uses already set for 2013 and beyond. The Olympic Park has been planned to provide a new metropolitan quarter that will trigger and shape a much larger redevelopment process across east London. None of this is really in doubt. London will have a great physical and urban legacy.

The Games will also reintroduce east London to London, reducing the travel times and psychological distances between central London and the east and bringing new investment into many eastern locations. In this respect, the 2012 Games play a key role in London’s spatial development. By increasing access to east London and making it more attractive, the Games enable London to break free from the constraint of an underserved east abutting substantial growth and congestion in the central and western sections of the city. If the London Olympics have a grand purpose, it is to rebalance London so it can grow more evenly in the future, better using available land for the right purposes. The Games will do for the whole of London what London Docklands did for financial services, providing a revitalized and connected east London where new things can happen in a city that is otherwise mature, congested, and full.

But east London is also the poorest part of London and one of the poorest areas of the U.K. It is an entry zone for impoverished populations seeking their opportunity in London, and has been for over 200 years. It is also a stable community of former industrial workers and their families, as well as the site of many small working town centers and communities.

East London needs a new economic narrative, with jobs and business growth, if it is to meet the aspirations and needs of this population. That new economy is emerging, albeit slowly. Digital, environmental, and health sectors are growing, and finance and business services, along with hospitality and education, are large employers. Retail and distribution remain strong. The new elements need to be fostered decisively if they are to truly emerge.

Former hosts of major world events stress the ability of such moments to help change perceptions of the host city or nation. In London, the identity of east London will change forever. But London as a whole faces major challenges and new competitors. One way to look at this is to observe the critical questions, or doubts, that the host nation must face as it plays host to the world. When the world comes to visit, a country’s greatest uncertainties are provoked.

Barcelona’s success in 1992 did not just take the form of the vibrant urban renewal that the Games triggered. It was the clear answer to the question, “Does Catalonia really have a future after Franco’s decades of repression?” Barcelona’s Olympics put Catalan identity, freedom of thought and expression, back in the public light and set a path for the city to be an international expression of Catalan prowess: more than a football club, more than a city—a capital of a reborn nation.

Sydney’s success in 2000 was to showcase Australian know-how and operational competence, and to answer the question, “Is Sydney really a world-class city?” It is no wonder that so many firms involved in Sydney’s Olympics are now global market leaders and are selling their talent and know-how all over the world, even while the local physical legacy has been slow to accrue.

Germany’s World Cup success in 2006 answered the question, “Is Germany actually friendly?” The world didn’t quite know. The Germans were wonderful hosts—gracious, generous, and kind. In 2006, the Winter Games tackled the question, “Is there life after Fiat?” Turin said yes, and the world began to agree.

“Is China really open to the world and does it want to be part of the global family of nations?” was the big issue behind the Beijing Olympics in 2008. It is and it does, but in its own way. “Is it safe?” was the question for the 2010 World Cup, and South Africa showed that despite all the doubters, it is actually remarkably safe, and certainly safe enough to visit.

In 2012, what is the looming question that London must answer? After the mighty economic crash, often attributed to London and New York excesses, and the biggest structural economic change and geographical rebalancing in the modern era, we must answer the question, “Is London still relevant in the new global order, and can it continue to be a genuine world leader?” Or, alternatively, “Are the great four centuries of London’s leadership now at an end as the world shifts east?”

The answers to these questions will be offered by Londoners over the next six months, and the world will decide whether it still believes our story. Only London can provide the answer. What is more, the question can only be answered with deeds, not with words. It is how the visiting world experiences and digests London that will answer the question, not what we say. The viewing global audience will be informed remotely, and it is what the broadcasters say and journalists write that will stick. Is London still a leader, and in what?

Perhaps it goes with the responsibility of being the first city to host the Olympics three times in the modern era that this question will prod until a conclusion is drawn.

London’s response to such a question might include many elements: the globally diverse population and the city’s extraordinary creativity and edge; its four regional universities that rank in the top ten worldwide, and many more that place high in ratings; the enduring world standards it meets in education, media, design, culture, science, medicine, and sport; the next act for finance and the professional services; and, adding to that, the unique historic strengths of language, business, culture, time zone, legal system, privacy, and spirit of freedom and enterprise. It remains a powerful recipe.

All this, and more, makes London likely to be a world leader for several decades yet.

But a city does not succeed in the 21st century simply by having a list of great assets. It also needs a strategy for and a story about its future. What is that strategy and story, and who is telling it?

There is a problem in telling the story currently because the gap between London’s potential and the current moment of austerity and economic uncertainty in the U.K. is very wide. London’s assets may involve its national prestige, future global roles, and enduring international attractiveness, but the national mood and national government policy are focused elsewhere. Restrictive visa access for workers and students and long queues at overcrowded and overburdened airports do not suggest a tolerant global city. At the same time, terribly unaffordable housing makes London anything but open. Added to that, images of riots, racially motivated murders, and terrorist attacks make London seem much less than the model of diversity that a global city needs to be.

Telling London’s future story over the next six months will be no easy job. But the Olympic Games provide a powerful backdrop and an organizing idea.

Why do the world’s best performers gather in London to compete in tightly controlled, rules-based contests where only talent, training, fitness, stamina, innovation, endurance, courage, and appetite count? Why do the best come to London to compete with the best in order to improve and inspire others to reach new standards, winning gold, silver, and bronze in the process?

Because London is a place that attracts the world’s best to compete with each other and to innovate and inspire in many other ways. In theater, science, business, media, retail, medicine, hospitality, design, architecture, and higher education London attracts the best to compete with the best. That is where invention and progress will occur in our global age, and that is why the world needs at least some global cities.

It is not so much that London is hosting the Olympics for the third time in just over 100 years and is the only city to do so. It is rather that London is Olympic in ways that few other places can ever be. Now there’s a story.