Brian Booth, of West Yorkshire Police Federation, made the comment as Home Secretary Priti Patel announced this week that a police covenant would be created, meaning that the importance of officers' welfare is now recognised by law.
Announcements for the new legal protection for officers came on Tuesday following months of discussion, while a consultation published by the Home Office revealed that more than 90 per cent of the 113 respondents agreed with proposals for the covenant.
Mr Booth praised the new laws, which would mean officers would not be fearing reprisals for taking time off for doctor's appointments, sick leave or for family holidays during the busy summer period.
"This will hold heads of department to account over staff welfare," he told The Yorkshire Post.
"There is a high number of divorces in police forces because of the inflexibility of the job. When you are due out at a family occasion then find out there has been a stabbing, you have to go. This impacts deeply on officers' families as well.
"When it comes down to it, it feels like we are servants of the Crown, not employees.
"When members of the public ring up because there has been a large gathering of people in their neighbour's garden, that's not going to be high on our agenda when there's a missing child down the road. We have had to deal with situations which are more for social services because care in the community has been stepped back.
"We are expected to do everything."
He added that ten years of austerity had bitten hard on the force - which recently told staff it faced a £30m gap in its budget for next year - and that the impact of cuts made from 2010 meant that police were "set up to fail".
Despite this, the Home Office is currently partway through a recruitment drive for 500 extra officers in Yorkshire & the Humber this year.
The new covenant places focus on physical protection for police staff, their health and well-being, as well as support for families.
Recent data revealed under the Freedom of Information revealed 391 individual officers at West Yorkshire Police took sick leave between April 2019 and April 2020 for mental health reasons, with acute stress responsible for 228 of those.
Some 167 staff at South Yorkshire Police took sick leave for mental health reasons in the period, while at North Yorkshire it accounted for 14,968 days' of leave. There is no data currently widely available for Humberside.
Mr Booth added that, in essence, the covenant meant a "happier workforce" serving the public.
"Morale in the police is very low right now and people are feeling very downtrodden. Having a happy workforce in the police is essential for the public."
Halifax MP Holly Lynch, whose father served as a police sergeant and who campaigns fervently for better funding and safety measures for officers, also welcomed the covenant but said the Government had taken too slow a pace in getting it ratified.
"I really welcome the police covenant but it was actually announced by the current Home Secretary's predecessor over a year ago now.
"We're looking to the Government to move the process forward at pace and share the detail of how the covenant will reflect our appreciation of brave, dedicated police officers and find practical ways of improving their wellbeing."
Home Secretary Priti Patel said: "The police and the families that stand behind them deserve special recognition. Their bravery and sacrifices are what keep us and our loved ones safe.
"I will put the police covenant in law to ensure they will always have the support of the nation."
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