Five people with mental health problems between them called the Metropolitan Police force 8,655 times in 2017, according to a new report.
It is an extreme example of the pressure police forces are being put under because of a national crisis in mental healthcare.
Officers often need to step in because more suitable services have finished for the day, HM Inspectorate of Constabulary and Fire & Rescue Services (HMICFRS) said.
This leaves police with tens of thousands of cases that should be dealt with by other agencies.
It comes at a time when they face their own challenges: increasing levels of knife crime and the ever-present threat of terrorism.
The report by HMICFRS is based on the response provided by police in England and Wales to people with mental health problems.
It said police in London receive a call about a mental health concern every four minutes and an officer was sent to respond to a mental health call every 12 minutes.
The calls could be from worried relatives or friends, requests from social services or GPs for police to make welfare checks, missing people, suicidal people or supporting victims of crime who have mental health problems.
The police should be the last resort, not the first port of call. Zoe Billingham, HM Inspector of Constabulary
HM Inspector of Constabulary Zoe Billingham said other services should stop relying on the availability of police.
"Over-stretched and all-too-often overwhelmed police officers can't always respond appropriately, and people in mental health crisis don't always get the help they need.
"The police should be the last resort, not the first port of call."
Police funding has fallen 19% in real terms since 2010 and officer numbers are down by more than 20,000 during the same period.
Chief Constable Mark Collins, the National Police Chiefs' Council lead for mental health and policing, said he shared the concerns raised by the report.
He added: "It is right that the police are there to protect those in immediate danger, but they shouldn't become the first point of call for those who need longer term mental health support and access to prevention measures."
Dr Paul Lelliott, lead for mental health at the Care Quality Commission, said: "People experiencing a crisis with their mental health need expert and prompt help. All too often this isn't available at the time and place that they need it.
"Although police officers generally do a good job in identifying and responding to those with mental health problems, they must never be considered a substitute for expertly trained healthcare professionals."
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A government spokesman said: "The NHS has worked closely with policing partners to reduce the use of police custody as a place of safety by 95% since 2011/12.
"We are investing £2bn in mental health services, including mental health liaison in A&E departments, and community crisis services, and NHS England will shortly be setting out its proposals to improve all mental health services in the long-term plan."