The Swedes are coming. As Europe lurches to the right amid financial and climate meltdown, a horde of cool-headed Nordic warriors are riding to the rescue. Sweden's EU presidency from 1 July will be greeted as a breath of fresh air after the Czech leadership, what with the latter's antics on climate change and arousal chez Berlusconi. What the EU needs is a whiff of sense and reason. And who better to provide it than the social-minded, climate-conscious Swedes?

Sweden still sets hearts racing across Europe. The "Swedish model" might bring up thoughts of a nubile blonde rather than a strong social state, but it is in the latter incarnation that my home country stirs the passions of left-leaning Europeans. Whatever Sweden does must be right, or so reason progressive politicians and Guardian journalists – not to mention scores of Swedes. But beyond this blue-eyed vision lurks a darker reality. Sweden's conservative coalition government has stood still as the financial crisis has engulfed the country. Jobs, social services and healthcare are eroding. The Sweden Democrats – the equivalent of the BNP – are on the rise. The social state is failing. The Swedish dream is no more.

Swedes were roused from this dream with the 1986 assassination of prime minister Olof Palme. Palme might have left behind "a country where no one was poor and no one had room for optimism" as Andrew Brown puts it, but it was Sweden's homemade financial meltdown of the 1990s that finally killed off the dream. Poverty was added to the pessimism. Savage cuts hit schools, unemployment rocketed, the krona sank – leaving the social system in a disarray from which it has not recovered. The conservative government at the time has lately been praised worldwide for its handling of the crisis. Actually the bankers were rewarded, not punished, while the rest of the country is still reeling from the cuts, selloffs and dashed dreams the crisis provoked. But the idea of a well-oiled Swedish model insulated from the shockwaves of capitalism runs on like a Volvo. The reality, like troubled, Ford-owned Volvo itself, is more globalised and gloomy than that.

Take healthcare. Swedes do not enjoy free public care: it costs to see a GP. That is, if you manage to see one. Queues are long and scandals rack the system. Psychiatric care, the source of many such scandals, has a near-medieval penchant for authoritarianism with few European equivalents. People are locked up for months for not taking medicine, given no therapy, and spat out of the system into despair and destitution. The mentally ill die in wards and in outpatient isolation. And they do not even have charities to turn to because state-run healthcare is supposed to work: this is Sweden, after all.

Those who do enjoy Sweden's second-rate public services are lucky. Undocumented migrants, who lack a "personal number", are barred from day-to-day healthcare. Foreigners do not fit easily into a social system built on the postwar notion of the folkhem, or people's home, whose rightful inhabitants are the native Swedes. Despite the xenophobic right's lack of electoral success, Sweden is divided between those inside the system and those outside it – including the asylum seekers now deported en masse to Iraq. But migrants should be happy to be here. This is Sweden, after all.

Even being in the system is less rewarding than it was. Unemployment benefits are falling behind those of other countries, and access to social security involves Big Brother-style controls most Europeans would abhor. The state's iron grip remains even as the care that used to go with it has gone. Swedes might lack Britain's profusion of CCTVs, but their lives are scrutinised by an armada of bureaucrats. A new law lets authorities tap all phone and internet traffic crossing the borders. Norwegian lawyers have sued over privacy infringement, leaving the prime minister perplexed – because in Sweden, the state is there to help us.

Just as Sweden was in the vanguard of postwar social democracy, it has since the 1990s become a neoliberal experiment. The experiment has failed, though this fails to register in Sweden itself. No waves rock the stagnant pools of officialdom: strikes are almost unheard of and the tabloids are too busy flogging diet tips to bother. The Swedes cannot let go of their belief in the system. Nor can many on the European left.

Admittedly, Sweden might seem a haven of tranquillity compared with other European states. But in the hunt for a humane social model, Sweden no longer provides the blueprint. Europe's progressives will have to construct something new. But to do that, those who let their minds drift northwards for inspiration first have to wake up: the Swedish dream is over.