Hopping on the spot at platform 19 of Radom bus station, dressed in electric-blue drainpipe jeans, Katarzyna tries to keep warm despite the icy drizzle and to make light of her imminent departure from her son David, as he tucks into the ice-cream she has bought him.

The 35-year-old is travelling to the town of Treia in the central Marche in Italy, where she’ll spend three months working in a restaurant, earning around €1,035 (£736) a month, cash in hand. “It’s six times what I’d earn in Poland – that is, if I could even get a job here,” she says, hastily drawing on a cigarette before her bus departs. David is taken home by his grandfather, who will look after him until his mother returns in June. The eight-year-old is what has become known as a “Euro-sierota” or “Euro-orphan” – a child left behind in Poland with relatives while its parents go abroad to work, a phenomenon from the era before Poland joined the European Union in 2004, but which has only grown since then.

Katarzyna, one of a very vaguely estimated two million Poles who are living and working abroad, has been doing a similar stint for 12 years. But in a study last week the World Bank warned that towns across eastern Europe, like Radom – which lies about 75 miles south of Warsaw – are growing prematurely old due to the extensive migration that has taken place in recent years, coupled with drastically falling birthrates. A glance at the statistics is enough to realise the demographic squeeze that is already taking place in Radom and will only worsen as its population both ages and shrinks. If the trend continues, according to the study, it will have a huge impact on pensions, the public purse and economic growth.

Statisticians have called Radom, with its 220,000 inhabitants and its roots in the middle ages, one of the fastest-shrinking towns in Poland and eastern Europe. The latest figures, taken from Poland’s Central Office of Statistics, show that in 2012 the proportion of under-17s was 17%, the 18- to 65-year-olds made up 64% of the population and those 65 and over, 19%. By 2035 those figures are expected to be 15%, 56% and 29%. And the trend of ever fewer births and an ageing population, supported by an ever smaller “productive middle”, is only set to continue. According to the World Bank report, if trends continue the entire region’s workforce can be expected to fall by almost 14 million by 2060.

Critically, 2012 marked the point that the number of deaths in Radom exceeded the number of births, making the front-page story of Friday’s edition of the local daily, Echo Dnia, seem particularly fitting. “The crematorium is nearly ready,” ran the headline over a report about how a new state-of-the-art facility run by a local company would open after Easter, offering employment to five locals and cremations for 650 zloty (£112).

Wlodzimierz Wolski has often been the one who has been forced to pick up the pieces when families have been separated as parents disappear to work abroad.

“I frequently witness the psychological harm that is done to hundreds of thousands of children whose parents have gone abroad, leaving them with grandparents or aunts and uncles,” the 64-year-old psychologist and director of Radom’s Centre for Crisis Intervention said. “In every case we’ve been made aware of, we contact the parents and urge them to come back.”

His most recent “Euro-orphans” case involved two teenage daughters left in the care of their overwhelmed grandmother while their mother and father went to London to work as a dishwasher and a construction worker. “The 14-year-old went off the rails and her grandmother came to us desperately seeking help,” Wolski says. “I rang the mother, who immediately expressed her shame but said she had had little choice but to go six months beforehand, because they could barely afford to feed the kids in Poland.”

Just two days later the mother had returned. The father is continuing to work on a UK building site and to send money back to his family. “For me, as for all Poles, it’s a very upsetting situation,” Wolski said. “And because it is a pure sense of need that is sending many Poles to work abroad, how it hurts to listen to David Cameron saying he wants to put restrictions on people working, even though he must realise how dependent the British economy is on Polish workers.”

At Radom’s job centre, its director, Jozef Bakula, talks of the daily struggle of living in a shrinking town – with its unemployment rate of more than 20%, and an average gross monthly wage of 3,411 zloty (£586), one of the lowest in the country (Warsaw’s is 5,077 zloty). “We have a huge shortage of certain types of workers, because they’ve gone elsewhere to find work that is better paid,” he said.

“The city is 10 GPs short, and we’re also missing IT workers, carpenters, plumbers and construction workers who’ve gone elsewhere to work. The situation is paradoxical because we have absorbed the cost of their education and training and often their upkeep, and then they go abroad and we’re no longer the beneficiary of their skills or the GDP they’re creating,” he said, from his fourth-floor office overlooking the city’s colourful communist-era housing blocks. When Bakula met his Dublin counterpart during a recent EU-funded study trip to Ireland, “they told us Polish accession is the best thing that could have happened to them, that ‘the brightest and best Poles came here’,” he recalled.

In contrast, he says, teachers, many of whom have been laid off as the city’s population has shrunk, are in abundance, along with many manual labourers, often metal workers formerly employed at the local arms factory whose skills have not been updated since communist times.

In the corridor where scores of job hunters – most of whom, Bakula said, are invariably unqualified or wrongly skilled – sit looking downtrodden and bored, the green screen flickers above them with an apparent abundance of fresh work opportunities, from pharmacists, to car mechanics, welders to turners – all vacancies that are hard to fill.

Bakula’s son is a trainee anaesthetist. He hoped he would choose to stay in Poland – “but I can’t stop him doing what he wants”, he said.

Government initiatives have tried to encourage workers to return to Poland. A returnee programme called Powroty (Returns), which offered incentives for people to come back and use their skills in Poland, was – even the government admits – a flop.

But Izabela Grabowska-Lusinska, professor at the Centre of Migration Research in Warsaw, warned against simplifying the issues, arguing that the Polish economy is still suffering from the “transformation shock” of switching from a centrally planned economy to a market-based one. “There is a huge mismatch between skills workers have and those the economy needs,” she said. “It’s very hard for the labour office to match those huge gaps, and so the decisions workers take to go abroad are very rational ones, even if the decision itself is often high-risk. Often migration is the only way in which the labour market can move and it’s a good thing.”

At a pensioners’ day centre on Henryka Sienkiewicza Street in Radom’s picturesque city centre, some played cards, while others sipped tea and chatted about their concerns for the future. Everyone had a story to tell of a loved one who had migrated abroad. Halina Swiderska, 67, its manager, broke down as she spoke of the hopes she had had for her handsome son, Tomasz, who she had helped get a job as a security guard in Cork 10 years ago. “But after just a few years he came back home in a coffin – he had had a brain tumour,” she said, wiping her eyes. Her grandson Dominik, seven, is still there, with her daughter-in-law who works for an American pharmaceutical company. Meanwhile she has managed to keep her two older daughters close to her in Radom. “But only because I subsidise them both with my 1,300 zloty monthly pension,” she said. Life – their attempts to have normality and to afford basic things – “was such a struggle for them, they have both decided against having more than one child”, she said. Other members tell very similar stories.

“Which leads to the question,” Swiderska said, “when we and our children are infirm, who will be left to look after us?”