The rise in the abandonment of infants across Europe is most visible in the spread of “baby hatches” or “boxes” across Europe, where unwanted infants are left anonymously.

The phenomenon was previously more prevalent among immigrants, but it is becoming more widespread among financially desperate members of the local population.

The hatches are sensor-activated so when a baby is placed, an alarm is activated and a carer comes to collect the child. Despite the practice being widely viewed as contravening the 1953 European Convention on Human Rights, of the 27 EU member countries, 11 countries still have "baby hatches" in operation, including Germany, Italy and Portugal.

In those countries where hatches are illegal, the number of infants abandoned in hospitals, clinics and churches has also risen, raising concerns among European charities, the UN and the European Commission that austerity measures and increasing social deprivation are the catalyst for the rise in child abandonment.

According to SOS Villages, a European charity that attempts to help families in financial hardship before abandonment occurs, in the last year alone 1,200 children in Greece and 750 in Italy have been abandoned. That is almost double the 400 children abandoned in Italy a year ago, and up from 114 children abandoned in Greece in 2003.

With the cost of raising children estimated to be 20-30 percent of an average household budget (per child) in Europe, more families are now struggling to cope with the costs.

The charity SOS Villages has reported that adoption rates in Greece and Italy have risen by 20 percent in the last two years, a sharp rise in line with the deterioration of the economy.

George Protopapas, National Director of the charity’s Greek division said that parents already struggling with keeping a roof over their heads are now barely managing to keep their children clothed and fed, if at all.

Protopapas cited the example of a four-year old child left at a nursery by her mother with a note that read: “I will not be coming to pick up Anna today because I cannot afford to look after her. Please take good care of her. Sorry."

According to Protopapas, the charity does not have exact figures for economic orphans, but over the next few years he expects “there will be more cases like this.”

“In the past year, SOS Greece has had a 150 percent increase in applications for all kinds of support, mainly [for] financial reasons, and 87 percent of applicants are Greeks,” Protopapas said.

Data from the Hellenic Statistical Authority shows that 27.7 percent of Greeks are now facing penury.

“For the moment most cases come from [the] low and poor class. Greek middle-class families are affected by the crisis but I believe they will be the victims in the coming two years. They will probably need serious support to survive,” Protopapas said.

His colleague, Stergios Sifnios, Director of Social Work in SOS Villages, told CNBC that in his 30 years of working for the charity he had not seen a societal crisis similar to this, prompting him to believe that things can only get worse.

“We are really afraid that in the future we will have a big number of families that cannot manage to keep their own children because of these problems. We are trying to be ready for this,” he said, but the government must keep on funding social welfare services.”

“[The government must] stop downgrading services in the name of the austerity measures.”

The phenomenon has not been lost on policy makers at the European Commission, the EU's executive arm. According to an EC report, 116 million people — and 20.5 percent of children — are at risk of poverty in the EU in 2012.

CNBC contacted the Commission’s office for Social Affairs but policy makers were unavailable for comment. An EU-funded program, "Daphne", was commissioned to assess which children were most at risk, and the economic instability of a household was cited by the report as a major factor in the increase of child abandonment.

“Many factors contribute to children being separated from their families. Research shows that the primary factors are everyday conditions e.g., poverty, unemployed parents, low or lack of income, a lack of material resources, and poor living conditions.”

According to Professor Kevin Browne of the Institute of Work, Health & Organizations at Nottingham University and one of the authors of the Daphne report, as economic conditions in Europe deteriorate, the human rights of Europe’s children are at risk.

“Infants and young children are those most at risk of being abandoned and the rates of child abandonment within the EU are concerning, especially in the current economic climate.”

“Article 7 of the United Nations Convention on the Rights of the Child, states that every child has 'the right to know and be cared for by his or her parents,' he said.

“When a child is abandoned, this right is violated", he said.