Magritte would have loved it – a tree growing out of the fourth floor of a towering office block at the junction of Nemanjina Street and Kneza Milosa Street.

But then, the building, which once formed part of Serbian military headquarters, is a ruin: a nine-storey heap of blackened concrete, buckled ceilings and contorted window frames. On one side is a hole that gapes open to reveal three entire floors.

The building stands directly opposite the office of Serbia's prime minister, Mirko Cvetkovic – a daily reminder that just 12 years ago his country was being bombed by the very European nations whose exclusive club Serbia now seeks to join. On Wednesday, his government took a giant step towards the realisation of that goal when police caught Goran Hadzic, scratching the last name from a list of 161 fugitives indicted for war crimes in the tearing apart of Yugoslavia.

Hadzic's arrest removed the last formal obstacle to accession talks. Yet many Serbs remain sceptical that a bright new European future really does beckon. "I don't think we can get into the EU," said a young restaurant manager striding past, who gave his name as Veljko. "We have a load of thieves in politics and a lot of problems with our economy."

Belgrade is deceptive. It is no longer the potholed, ill-lit, gangster-ridden city it had become by the end of Serbia's wars. The red plush and flock wallpaper have long gone from the once dingily evocative, Soviet-era Moskva hotel and the clients in the pavement cafe outside are well enough dressed.

Yet Miroslav Zdravkovic, who runs the website ekonomija.org, estimates that average real incomes in Serbia are today no greater than they were in 1971. Before it fell to pieces, Yugoslavia, along with the rest of communist eastern Europe, had endured a decade of economic stagnation. Then came the wars and, for Serbia, painful sanctions.

During the 2000s, Belgrade and the next biggest city, Novi Sad, may have recovered. But much of the rest of the country did not.

Todor Gole owns a firm that produces seats for buses at Priboj in western Serbia. "In 2003 we had 40 employees. Today I and my family are the company's only workforce," he said. Like many others, he blames policies that allowed firms to be privatised and then asset-stripped. "I've seen companies being privatised and then closed – the companies I did business with in the late 1990s," he said.

Serbia, like other countries, has had to contend with a severe global recession. "There are places where real incomes are at the same level as in the 1960s," said Zdravkovic, "and some are below that." His calculations suggest the hapless citizens of Bor, an eastern mining town, are as poor today as they were in 1939.

A fifth of Serbs are unemployed and the average net salary for those who are not is between €300 and €350 a month.

Dressed in a neatly pressed suit, collar and tie, Milos Tomsin sits outside a bar on a leafy street in central Belgrade nursing a beer and a fierce sense of injustice. He returned to Serbia in January after losing his job abroad. "I've not had a single decent offer in six months," he said. At the age of 40, Tomsin finds himself living with his mother in a flat in the suburbs. "For any adequately remunerated job you need political or family connections that I don't have," he explained in flawless English. "There's a glass ceiling in Serbia for people like me at around €600 a month."

Serbia's economic difficulties ought logically to translate into burning enthusiasm for EU membership and the open borders and outside investment that it would bring. Yet, as it has edged closer to talks on accession, popular support for EU membership has fallen steadily.

A government-commissioned poll conducted in June found that only 53% of those questioned would vote for entry. As recently as November 2009, the same pollsters, using the same question, had obtained a figure of 71%. The results of another, privately ordered survey in March suggested less than half the population supported entry. Several factors appear to be at work. Goran Nikolic, who works for a government research institute, said fear of yet more privatisation was an important consideration. "More than half a million people are employed in the public sector and they are frightened of losing their jobs: to work for the public sector is a privilege," he said.

Many worry that, having surrendered their war crimes suspects, the Serbs will be asked by Brussels to make unacceptable concessions to their neighbours. "Serbia has problems with Kosovo. It has problems with Montenegro, with Bosnia and Croatia", said Nikolic, "and in all these cases the west's perception of the issues is different from that of Serbia."

A particular fear is that the EU will demand Serbia recognises Kosovo and, as with Cyprus for Turkey, it will become either an insuperable obstacle or a convenient excuse. "How can we recognise [Kosovo] when it goes against our constitution and all historical and legal logic?" asked Tomin.

The head of the government's office for EU integration, Milica Delevic, said she detected "a growing belief that the EU will become more resistant to taking in new members" and she added: "I think it's important that the EU sends a message that it understands how important a step [the arrest of Goran Hadzic] is."

But, she argued, Serbians' waning appetite for Europe was to be expected. "If you look at every country that has approached accession, people start out with great enthusiasm and then, later on, they find out that they have to give something up and so they make a rational appraisal of their interests."

Serbs have had to give up more than most, including more than 100 of their fellow citizens whom the majority do not regard as war criminals (a poll showed only 34% supported the handing over to the international war crimes tribunal of the Bosnian Serb general Ratko Mladic, widely regarded in the rest of Europe as an embodiment of military savagery).

Yet, paradoxically, the very polls that show flagging support for EU membership also show mounting enthusiasm for the means of achieving it. The results of the government's latest survey indicated 85% support for the necessary reforms – a figure seemingly at odds with the view that Serbs are becoming less keen on Europe as they find out about the sacrifices involved.

But then the demand that gets most backing, according to Delevic, is the commission's insistence on rooting out corruption. So the poll findings may be less paradoxical than they appear.

The promise of EU membership can be a powerful incentive for combating cronyism and patronage, but it loses all effectiveness after accession. Consciously or not, Serbs may be sending a message that they do not want the corruption that is rife in their country to be locked in, as appears to have happened in Romania, Bulgaria and perhaps Greece.

"We have to become members of the EU", said Zdravkovic, "but we have to become a better country first."