The European Union is experiencing a steep rise in the number of Kosovo citizens smuggling themselves into the affluent bloc, with 10,000 filing for asylum in Hungary in just one month this year compared to 6,000 for the whole of 2013.

It follows a relaxation of travel rules allowing Kosovars to reach EU borders via Serbia and has coincided with political turmoil and street unrest in Kosovo fuelled by poverty, high unemployment and economically debilitating corruption.

The United Nations High Commissioner for Refugees (UNHCR) said hundreds of Kosovars had slipped into Hungary and asked for asylum in the first eight months of last year, only for the number to rocket to 21,000 between September and December.

Hungary’s State Office of Immigration and Nationality said that of 14,000 foreigners who had sought asylum since the turn of the year, 10,000 were from Kosovo, a small, ethnic Albanian-majority state that declared independence from Serbia in 2008.

“We have visited several reception centres in the past two weeks and most of the Kosovars we talked to said they came because of extreme poverty and total lack of perspective,” said Erno Simon, a UN refugee agency spokesman in Budapest.

Over the past few days, crowds of people were seen boarding night buses from the Kosovo capital Pristina bound for Serbia’s capital Belgrade, more than halfway to Hungary.

Among them, 18-year-old student Vilson Beqiri said he would take a second bus from Belgrade to the northern Serbian town of Subotica and then cross the border into Hungary illegally.

“We’ll meet some other people there (in Subotica), pay them, and they’ll lead us to Hungary,” he said. “God willing I’ll be in Germany by tomorrow evening.”

We have visited several reception centres in the past two weeks and most of the Kosovars we talked to said they came because of extreme poverty and total lack of perspective

The exodus appears to have been abetted by an EU-encouraged easing of travel rules in Serbia, which since 2012 has allowed Kosovars to enter with Kosovo-issued documents that Belgrade previously rejected given that it does not recognise its former southern province as independent.

It has also coincided with political turbulence in Kosovo, which held an inconclusive election in June and only formed a new government six months later.

Last week, police fought running battles with protesters lobbing rocks and petrol bombs during anti-government demonstrations stirred by joblessness and corruption.

Rados Djurovic of the Asylum Protection Centre NGO in Belgrade said people smugglers may have found new routes to spirit migrants from Serbia into Hungary – a well-trodden path for Syrians, Afghans and others trying to reach Western Europe.

On Monday, 250 illegal migrants from Kosovo were stopped by Hungarian police without valid documents on a train from Budapest to Vienna.

Almost all asylum applications are rejected as migrants cannot show they are fleeing war or persecution, but applying staves off immediate deportation while their cases are being processed. In the meantime, many will give overstretched immigration authorities the slip and push on westwards through the EU’s borderless Schengen zone under the radar.

Most would hope to find work in the grey economy in wealthy Western Europe, hooking up with relatives and friends until they can ultimately legalise their stay.

Hungary’s immigration agency said 40-50 per cent of asylum applicants would normally leave the country within 24 hours, and a further 30-40 per cent within three to 10 days.

Around 700,000-800,000 Kosovars already live and work in western Europe, mainly Switzerland and Germany – a diaspora that originated with an exodus from repression and war with Serbia in the late 1990s and then stubborn poverty in the 15 years since.

Kosovo declared independence in 2008 and is recognised by more than 100 countries. But Serbia’s refusal – backed by UN veto-holder Russia – to do so has impeded Kosovo’s international integration and therefore its economic development.

Kosovo Interior Minister Skender Hyseni said the government was at a loss to stop the emigrant wave. “[We] could stop this process by simply putting a roadblock at the border crossing points, [but] then the government would be accused of violating a fundamental human right.”