Chief Constable Olivia Pinkney says officers can spend half their shifts working on behalf of other services.
As a result, crime victims are being "failed" and the criminal justice system is now in "crisis", she says.
It comes as BBC News has revealed police are taking longer to respond to crimes and are charging fewer suspects.
Our reports have heard from victims who say they have had to turn detective to solve their own crimes. We also visited one cul-de-sac where there have been 10 burglaries on the street, or in neighbouring streets, in a year-and-a-half.
We asked the National Police Chief Council to respond to our findings.
Ms Pinkney, chief constable of Hampshire and the Isle of Wight Constabulary, says she wants all officers to be freed from attending incidents that "are not for the police service to lead upon".
On average, she says officers attend 54 mental health incidents every hour and spend three hours waiting with people before health professionals then take over.
"Come and sit in a police control room at half past three on a Friday afternoon, and the number of calls that come in and say 'we haven't been able to resolve this in health, in children's social care, so we'd like the police to own this risk until Monday'", she says.
"It all lands on your desk because we're here 24/7, we answer the phone."