Police officers have reported being driven to breaking point by the dual pressures of staffing cuts and rising demands, with a survey finding eight out of 10 had felt stressed in the past year.

The survey by the Police Federation, which covers England and Wales, is part of a campaign to pressure the government to fund more officers on the beat after years of cuts.

It found that 79% of respondents said they had felt stressed or anxious in the last 12 months, with 94% of those saying their policing duties had caused these feelings or made them worse.

Nine out of 10 respondents thought there were too few officers to meet the demands on police, six out of 10 had experienced a traumatic incident in the last 12 months, and about four in 10 said they saw their role as police officers as “very or extremely stressful”.

DC David Stubbs, 40, from the Staffordshire force, said he sought counselling after stress left him unable to sleep. “I was feeling like I was banging my head against the wall, and swimming in mud,” he told the federation.

Stubbs said he was going from one tough job, such as a car crash, to another, such as a stabbing, with no down time during his shift, and with rest days and time off cancelled as his force struggled to cope with the loss of a third of its officers. “You start playing over jobs in your head and not sleeping.”

PC Dan Gaunt, from the North Yorkshire force, was diagnosed with post-traumatic stress disorder after the death of a baby in an accident. He said he delayed asking for help and did not want to take sick leave because it would have placed added pressure on his already stretched team.

“It took a couple of months for my brain to decide it hadn’t coped properly,” and then another couple of months for therapy to start, he said in the federation’s report.

The policing minister, Nick Hurd, said: “The home secretary and I have been crystal clear that policing’s greatest asset is its people, and we are determined to ensure that forces have the support and resources they need to protect the public.

“Parliament has approved our funding package for next year, which will increase investment up to £970m, including money raised through council tax. This funding settlement recognises the demands on police forces, and police and crime commissioners are already setting out plans to recruit more officers as a result.

“We take the wellbeing of police officers and staff very seriously, which is why we launched the frontline review to listen to their concerns and have invested £7.5m in a new national police wellbeing service.”

Ché Donald, a vice-chair of the federation, which represents officers in England and Wales, said: “Since 2010 the government has continued to slice away at the service, leaving us with almost 22,000 fewer officers now than we had then. The shameful legacy of austerity is an overstretched service staffed by stressed and traumatised officers.”

The Conservatives have said since 2010 that policing received enough money, a position maintained by both Theresa May while she was the home secretary and her successor, Amber Rudd.

When Sajid Javid became home secretary last May he tried to thaw relations by acknowledging that policing was under strain and needed more resources, citing as a sign of his good intent the fact that his brother was a senior police officer.

Donald said: “I compel the home secretary who claims he ‘gets’ policing to read this report and act on it, and when he is finished reading it, share it with the Treasury. The once revered British model of policing is currently on its knees and facing extinction. We need to act now to save it.”

Andy Rhodes, who leads on officer welfare for the National Police Chiefs Council, said: “ It is vitally important that they receive support and care because as a society we have an obligation to look after the men and women whose job it is to keep us safe.

“We will make an evidence-based case for increased investment at the upcoming government spending review that takes into account the increased demand on officers and staff. It will also consider other changes that will benefit those working in policing and the public, such as cutting bureaucracy and improving technology.”

• This article was amended on 13 February 2019 to make it clear that the Police Federation covers only England and Wales. It was further amended on 15 February 2019 to correct text reporting that “about four in 10 [officers] said they saw their role as … ‘very or extremely successful’”. This final, crucial, word should have been “stressful”.