Jean-Claude Juncker may not be the right answer, but his candidacy for the presidency of the European commission is at least a response to the right question. The process by which he rose to lead the European People's party list – which then emerged as the largest group in the European parliament – was an attempt to engage voters in the European decisions taken in their name. As such, it confronted the central political issue of our times.

We live in a world of increasingly global problems, ineffective national solutions, and consequent disillusion with democratic politics. These tensions will ultimately prove as great a threat to our democracy and our values as the totalitarian regimes of the 20th century. Who cares about pretentious, powerless politicians? Powerlessness is stealthy, insidious and corrosive to our belief that politics matters. At least Europe has attempted to respond by electing its supranational legislators.

It is, though, a work in progress. Europe is full of talk of the "democratic deficit", even though EU institutions are the only transnational bodies with any elected component. Nor are the voters impressed. Even in Europe, there is scant understanding of the new transnational realities. The European parliament elections showed a yearning for simple, nationalist solutions.

Nigel Farage, Geert Wilders and Marine Le Pen are tribunes of nostalgia for national certainties. Yet scarcely any problem that people care about passionately is any longer susceptible to a purely national solution, even by a country as big, powerful and besotted with the perfume of sovereignty as the US. Yesterday's American hubris is today's Iraqi disaster.

Conflict resolution? Most recent conflicts have begun within societies, not between them. Last week's UN report noted that there are now 51 million refugees and internally displaced people across the world, half of them children. This was the highest level since the second world war, and mainly due to internal conflict in Syria, South Sudan and the Central African Republic.

Yet the UN is no nearer to developing a legitimate template that can impose order in the increasingly common phenomenon of the failed state. Afghanistan, Yemen and Sudan have all been horrible warnings of what can follow from internal collapse, all with consequences far beyond their own frontiers. Ominously, Pakistan is on many experts' danger list, and it is a nuclear weapons state.

Even an issue like wealth and income inequality, once the meat and drink of class-based national politics in the old democracies, is not immune. Inequality is likely to grow, as Thomas Piketty has argued. National solutions will not work. High tax rates in one country are liable to be undercut by competitor countries, sometimes gleefully and deliberately, as in the case of George Osborne's explicit decision to cut corporation tax rates. The only solution is international agreement on tax avoidance, evasion and minimum tax rates. Goodbye nation state.

Take the prosperity brought by large-scale mass production. The US is so rich in part because of its huge domestic market. If we want our European companies to produce at scale, they have to be able to make the same product for the whole European market. For such a single market to work, every national market has to have similar consumer safety, health and environmental standards. That means at least Europe-wide – and maybe soon transatlantic – rule-setting. Goodbye nation state.

Then there is clean water and unpolluted air. Climate change alone makes the case for international action: without it, we are heading inexorably for such extreme weather events that our prosperity will be cataclysmically undermined. Ask the insurers: one group of private companies only too aware of the rising costs and damage of climate change.

Take even an area traditionally central to the nation state, such as crime. The European arrest warrant and speedy extradition are responses to the easyJet age. Cybercrime disrespects frontiers as readily as air or sea pollution. Fraud in London may begin in Singapore, and involve counterparties in Zurich. Policing is international, or it is flat-footed.

If we cannot grasp these global issues – fundamental to our future prosperity and to our belief in the efficacy of the public realm – the disillusion with national politics will fester. When problems are global, solutions must match. Power is increasingly going to be wielded supranationally. That, in turn, brings the challenge of how to make politics work across language and cultural barriers.

This is not a counsel of despair. We have solved global problems such as the hole in the ozone layer. There are also examples of successful, multilingual democracies that provide a model for the public accountability of international power: India, Switzerland and Canada. (I could add Belgium and Luxembourg, but that is more contentious.) Language barriers may even melt as voice-recognition technology gives everyone a hand-held interpreter.

But we need a public debate about where the real problems in our democracy lie, rather than hankering for some mystic past in which powerful nations resolved simple problems with the smack of firm government. David Cameron needs to spell out some home truths to his own party, and start to provide some answers himself.

The greatest democratic problem today is the weakening power of the nation state faced by threats stretching beyond its borders. The nation's weakness is fatally wounding the prestige of its political elites. Pity the mediocre Juncker, for he carries all the expectations of this new and frightening world.