Rising threat levels from the likes of extremism and organised crime has left a police force at "tipping point" after years of funding cuts, its chief says.
The chief constable and Police and Crime Commissioner (PCC) of Avon and Somerset Police said a further £17m of savings were required by 2021/22.
They said the force "cannot sustain further funding cuts without extremely serious consequences".
But, the Home Office said the force had got £4.5m in extra funding this year.
In the letter and a report sent to police and fire minister Nick Hurd, Chief Constable Andy Marsh and PCC Sue Mountstevens said the force has had to make £65m worth of cuts since 2010 and the extra £17m was needed to balance the budget.
They said demands on the force had increased, including the threat from extremism and organised crime.
Mr Marsh said the number of "complicated and sensitive" crimes such as sexual exploitation, violence against people, domestic abuse, rape and hate crime had risen from 20,000 to 40,000 in the past seven years.
He added there had also been an big increase in the number of "none crime" matters, such as missing people, that police have to deal with.
He said the savings required equated to 300 police officers, and services including patrol work, neighbourhood policing and call handling would be the first to suffer.
Ms Mountstevens said: "We have reached the point where enough is enough and policing in Avon and Somerset cannot be stretched any further."
She said it was "important" the government "knows what we face locally and understand the consequences of our current situation and the implications on the service we are able to deliver as a result".
A Home Office spokesperson said the government had "protected overall police spending in real terms" since 2015.
They added Avon and Somerset Police had received £4.5m more funding this year compared with 2015/16, and the government had announced additional funding for counter-terrorism policing.