Detective Warren Hines says he is aware of sergeants allocating work "on the basis of who is the least tearful that morning".
A decorated senior detective says an increasing number of police officers are contemplating suicide because of the strain being put on forces across the UK.
The warning from Detective Inspector Warren Hines comes as the National Police Chiefs Council (NPCC) calls on the Government to increase police funding.
In an exclusive interview, DI Hines, who heads up one of six murder squads in the West Midlands, told Sky News that police forces simply cannot cope with the work they are being asked to do because they are not properly resourced.
Budget cuts imposed under the Conservative government have seen more than 19,000 police posts shed since 2010. DI Hines said: "We really are at a point now where we can't cope with what we're expected to deal with. Sickness and mental health problems amongst my colleagues are rife.
"We've got examples of police officers who have been conveyed to hospital from work because they've had a meltdown.
"I'm aware of incidents where sergeants in our public protection units are allocating work on the basis of who is the least tearful that morning when they get to work."
The veteran officer said many forces had been forced to cancel annual leave and increase working hours following a series of high-profile major incidents.
There have been four terror attacks in three months - at Westminster Bridge, Manchester Arena, London Bridge and Finsbury Park - as well as the Grenfell Tower fire.
Officers from West Midlands were sent to the capital this week to help out in the aftermath of the latest attack. DI Hines said many of his colleagues are now at breaking point.
"In the last 15 months alone, around 80 officers in the West Midlands force have been referred to the National Police Federation Welfare Support Programme," he said.
"Those are people who are undergoing a significant mental health crisis.
"They're experiencing suicidal thoughts and tendencies and they are at risk of doing something really serious to hurt themselves, and this is only as a result of the pressures that they are being put under." The Government has promised that forces will not face any further budget cuts for the remainder of this Parliament, but the NPCC says the current "flat cash" settlement for policing means force budgets will fall in real terms.
Dave Thompson, Chief Constable of West Midlands Police and the national lead on finance for the NPCC, said: "Taking into account inflation and cost pressures, there will be less money every year for forces on top of real-terms cuts of 18% since 2010.
"Many forces are now using considerable reserves to maintain current staff numbers that, when spent, will see numbers falling even further."
The PFOA run The Welfare Support Programme on behalf of the PFEW and are currently supporting 281 officers including 36 officers and 2 members of the public from the recent terrorist attacks!