Business leaders and unions have called for mental health to be given the same weight as physical first aid in workplace legislation.

An open letter urging Theresa May to prioritise manifesto pledges to act on mental health has been signed by some of Britain’s biggest employers, including Royal Mail, WH Smith, Mace, Channel 4 and Ford, as well as the Unite union.

May said last year she would shake up mental health service provision, describing the shortfall as “one of the burning injustices in our country”.

The letter calls for the government to overhaul health and safety rules to equip first aiders to deal with early signs of mental health problems, as much as handing out bandages or performing CPR.

It said employers’ duty of care should mean “equalising their number of mental health first aiders with physical first aiders” and trying to “break the stigma of mental health in the workplace”.

The letter argues that the cost should not be an issue to employers, as workplace mental health issues cost the UK economy almost £35bn a year, with 15.4m working days lost to work-related stress, depression or anxiety. It adds: “The cost is not just financial, because left untreated mental ill health impacts a person’s relationships with friends and family and ultimately their quality of life.”

According to Mental Health First Aid England, a social enterprise that provides awareness training, one in six people of working age will experience mental ill health including depression, anxiety or issues relating to stress – almost 5 million people.

MHFA said ensuring first aid support for mental health would make a big difference to how health as a whole was perceived. Simon Blake, chief executive, said: “The principle [of physical first aid training] is enshrined in workplace law.

“Just as a physical first aider might know how to use CPR to save a life or put someone in the recovery position, a mental health first aider also uses a set of skills to guide a person who is struggling or in crisis to a place of safety and support.”

More than 300,000 people in England have been trained in mental health first aid, to recognise the signs and symptoms of common issues, according to MHFA.

Employers who have implemented such training include WH Smith, whose chief executive, Stephen Clarke, a signatory to the letter, said: “We are calling for this legislative change, alongside many other leading employers, as we firmly believe that everyone should have access to first aid support for their mental health regardless of where they work.”

Thames Water, which has more than 350 employees across its organisation now wearing green lanyards identifying themselves as mental health first aiders, said it had seen a 75% reduction in work-related stress, anxiety and depression over the last five years. with more occupational health referrals for stress, anxiety and depression than for physical illnesses.

A study this year by the charity Mind showed that almost half of UK workers have experienced a mental health problem at their current job. Fewer than half of those had opened up to their employer, suggesting that as many as one in four workers were struggling in silence with issues such as anxiety, stress or depression.