The continent of siestas and vacances, Europe used to pride itself on its healthy work-life balance. But as surveys show that increasing numbers of Europeans struggle to stop work encroaching on their private lives, governments are pondering whether the state should do more to protect workers from stress.

Unions have repeatedly raised concerns that the advent of smartphones and email have resulted in a workforce always on call. In several countries, including Austria, Denmark and the Netherlands, employers are legally obliged to assess workplaces for the risk of psychological stress.

Now the German labour minister, Andrea Nahles, has commissioned an in-depth study to establish a definition of work-related stress and calculate its economic cost. "Noise can be measured in decibels, but with stress it is much harder to say what it actually is," a spokesperson said. "So we are trying to establish a scientific foundation."

The study could pave the way for an "anti-stress act" as proposed by Germany's metalworkers' union. The draft includes a demand that employees should be protected from being "permanently reachable by modern means of communication" such as email or mobile phones.

Politicians from the Social Democratic party, the Greens and the Left party have lent their support. Yasmin Fahimi, the secretary general of the Social Democrats, said "a reliable end to the working day is a human right", while the head of German health insurance company Barmer said a law could "protect our health from permanent stress by setting clear standards".

According to a recent study by a psychotherapists' body, psychological illness is to blame for 14% of missed working days in Germany – a 50% increase over 12 years. Every second early retirement is caused by psychological illnesses.

Meanwhile, the OECD's better living index[http://www.oecdbetterlifeindex.org/topics/work-life-balance/] from 2010 showed that people across Europe were finding it harder to stop their work life from encroaching on their private life. Another recent EU-wide study claimed that Germans worked an average of 2.8 hours of unpaid overtime a week, more than any country on the continent, though other surveys have shown that northern Europeans work fewer hours a week than those in Greece.

Critics of the anti-stress law proposal say European workers are already adequately protected by existing legislation, such as the EU's working time directive.

Austria introduced an anti-stress law in January 2013, requiring all employers to have their workplace environment and atmosphere assessed for stress factors by an occupational psychologist. Conditions such as working hours and intrusion into private lives are likely to be included in an assessment, but "it is not explicitly stipulated", according to the Austrian work psychologist Veronika Jakl.

"The psychologist who goes in to assess the workplace has the responsibility to look at these things. If an employee mentions [intrusion into private life] to the psychologist then they would include it in their assessment for the employer. It is then the employer's responsibility to do something about it and enforce measures to reduce the stress," she said. "The company is obliged to write down all of the stress factors and then document which measures it will take. These will then be monitored in future assessments."

Belgium and the Netherlands recently moved to explicitly list burnout as one of the health risks from which employers are obliged to protect their workers.

In Germany, big employers such as Daimler and Volkswagen have come up with their own proposals to combat work-related stress. In 2011, Volkswagen agreed to stop its Blackberry servers sending emails to some employees outside working hours. From this August, Daimler gave about 100,000 workers the option of having their emails automatically deleted while they are on holiday.

The anti-stress law mooted in Germany would set a new precedent, as employers would be legally obliged not to contact employees out-of-hours. Whether it will become law is far from clear. It remains controversial even in Social Democrat circles, and a number of politicians from Angela Merkel's party have voiced opposition. "What are plumbers meant to do when you've got a burst pipe after 6pm?" asked the CDU politician Michael Fuchs.