It's early Saturday evening in Bristol. In one of those vehicles that looks like a reinforced minibus, a two-person police response team is doing the rounds of the suburbs to the city's north-east. PC Beth Hawke and PC Dan Heyward see themselves as police "activists". By which they mean, as Hawke puts it: "We like to go out, and we like to nick people."

But Hawke's clear-cut view of what working a beat should be like is coming under threat. Earlier this month, the Police Federation – which represents 124,000 officers – announced the results of a ballot on whether it should push for police to have "industrial rights": in plain terms, the ability to strike. Many more officers voted in favour than against (45,631 to 10,681), but because turnout was lower than 50%, there was no official mandate. For the federation, however, the result offered concrete proof of its members' anxiety about budget cuts, changes to officers' terms and conditions and the dire state of morale.

As Steve Williams, chair of the federation, sees it, the fact that around a third of Britain's police voted in favour of industrial rights shows they are "very angry and disappointed … people are being overstretched, and the perception of attacks on their pay and conditions is grinding them down". Indeed, last month a survey of 1,400 officers from the Avon and Somerset force revealed that 95% have no confidence in government plans for the police, which suggests that most of them may be not only stressed, but quietly seething. Just over half said they "would consider looking for alternative employment".

I am shadowing Hawke and Heyward a week before the result of the ballot. Given that the Avon and Somerset constabulary's press office has prohibited them from talking about budget cuts and morale, there is something of an elephant in the back of the van.

Hawke is 25 and from Bridgend, South Wales. She used to play women's rugby for her home country, and uses impeccable cop-speak to tell me that the changes to police conditions and pensions "are of some concern". But she insists she loves her job. She has recently applied to work in something called the operations unit, where she would specialise in underwater searches and "dirty body removal". She explains the latter thus: "You deal with bodies that have been there for anything longer than a week, really, and they are in the process of decomposition."

When asked about the most dangerous aspects of their jobs, neither constable misses a beat. "You can be searching somebody who has HIV/Aids, or hepatitis," says Hawke. "You'll empty a rucksack and it'll be full of uncapped needles. That, for me, is the biggest fear: a fear of infection. And we regularly come across people with weapons: anything from, like, hammers, knives …"

"I had a meat cleaver come through a door at me once," says Heyward, aged 36. "I was knocking on a door. I could hear something behind it – and the next thing, the blade actually came through the door. We backed off: we called for our armed response unit."

Nothing nearly so dramatic happens tonight, though it has its moments. At around 6.30pm the two officers are called to a flat above a shopping parade in the Henbury area. An ambulance is on the scene, because the man recorded as living there has been making 999 calls, which have suggested some kind of breathing problem. Peering through the letterbox, all anyone can see is an enveloping darkness and the flickering light from a TV.

Eventually, Hawke and Heyward decide they have no option but to break down the door – whereupon they discover an emaciated man, surrounded by at least 20 cans of beer and empty bottles of whisky, apparently oblivious to the fact that most of his electricity has short-circuited, and the flat is freezing. In the kitchen, there is a smattering of rotting food. It transpires that he has been released from prison after serving time for drink-driving, and shows all the signs of being not just malnourished, but having mental-health issues.

Dealing with late-night trouble in the centre of Bristol. Photograph: Sean Smith for the Guardian

This grim scene highlights one aspect of the police's current predicament: as social services budgets are slashed, it is ordinary officers who find themselves clearing up the mess. "We've seen a massive shift in the last 12 months," says Hawke, "especially in relation to mental health." She reckons that law-breaking now accounts for no more than 20% of her work.

These are turbulent times for ordinary police officers. Like so many public sector workers, they are in the midst of a two–year pay freeze and facing increased pension contributions. By 2015, the Home Office hopes to have cut its grants to police forces by around 23%, meaning that the organisation of many constabularies is in flux; numbers of officers and civilian staff are tumbling.

There are already 11,500 fewer police officers than at the time of the last general election, and around the same number of civilian jobs in the force have been shed. Official research suggests that in two years those losses will each have grown to around 16,000. Many police stations are being closed altogether, or to the public: in London, 65 are shutting their front desks, which will be moved to post offices and – bizarrely – supermarkets. Already, some forces are in a delicate state: a report last year by HM Inspectorate of Constabulary warned that the Met, Lincolnshire, and Devon and Cornwall might eventually be faced with an inability to provide a "sufficiently efficient or effective service".

At the same time, the government is in the midst of radical reforms to policing in England and Wales. In the autumn of 2010, the home secretary Theresa May announced a comprehensive review of officers' terms and conditions, to be overseen by Tom Winsor, the lawyer who spent five years as the chief rail regulator. He reported back in two stages: "Winsor I", focusing on short-term alterations, appeared in April 2011, and "Winsor II", a package of more thoroughgoing changes, followed a year later. At which point, it all went off, with the Police Federation claiming the proposals threatened to "undermine the very foundations of British policing and the public we serve".

Winsor has since been appointed to the role of HM chief inspector of constabulary, and most of his key reforms are on the way. The starting salary for a police officer will soon be cut by £4,000 to £19,000, though recruits with some experience of policing – such as community support officers – will initially earn around £22,000. (To put this in perspective, McDonald's pays its trainee managers between £18,500 and £21,500.) The "competence-related threshold payment", whereby most officers earn an extra £1200 a year, is for the chop. Higher ranks will be opened up to outside candidates – meaning that some senior officers will never have been on the beat. There are also plans for "compulsory severance", for the first time giving chief constables the power to sack officers – something currently being negotiated via the Police Arbitration Tribunal, and due to be confirmed by July. For the Police Federation, this issue threatens to turn constables into mere employees, imperilling the principle that – to quote the renowned judge Lord Denning – they are "answerable to the law and to the law alone".

These are not the only elements of May's reform drive. English and Welsh police forces are now overseen by 41 elected police and crime commissioners. Last month, partly in response to belated revelations about the Hillsborough disaster, the home secretary announced a new regime to safeguard police integrity, built around an official code of ethics and an expanded and strengthened Independent Police Complaints Commission. Meanwhile, some constabularies have been trying to cut costs by outsourcing elements of police work to private companies.

Those pushing for reform are fond of quoting a particularly sobering statistic: in the 18 months to December 2012, seven of England's chief constables were either forced to resign, suspended, sacked for misconduct or placed under criminal or disciplinary investigation. Amid all the noise about the future of the police, one thing is obvious: the view of the force as "the last great unreformed public service", first suggested by David Cameron back in 2006, has become common media currency.

Dry numbers, though, tell you less about the state of things than conversations with serving officers. Hacking down the starting salary, many claim, will deter those who become police officers in second careers, depriving the service of people with valuable life experience. "I wouldn't join on £19,000," one officer says. "I couldn't. If you've got a family, there's no way. It just prices people out."

Avon and Somerset's deputy chief constable, Rob Beckley, is sanguine about the cuts, the state of morale, and most of the Winsor reforms – but on this point, his judgment is clear: "What worries me is that we have, in latter years, recruited people with great life experience from other professions. They often take jobs in the police in their 30s and 40s, and they add an awful lot of value." If starting salaries are too low, he says, "you simply won't get people in". And does he think that's a danger? "Yes. Yes I do."

On condition of anonymity, one constable with 16 years' service in the Midlands, admits that morale is "really dire". He voted "yes" in the industrial-rights ballot, not because he wishes to strike, but "to show my feelings, that enough is enough".

"It feels like we're constantly under attack from the government," he says. His force has just emerged from a long and morale-sapping recruitment and promotion freeze. Police buildings have been sold off, and the vehicle fleet has been cut: 999 response teams have been taken out of local police stations and squeezed into a central "hub" – which saves money, but means they lack local knowledge.

The Winsor reforms, he reckons, are "all about saving money – it's got nothing to do with improving skills or professionalism. It just seems to be about making us work like robots, for less money." And they are playing their part in what he claims is a huge sapping of officers' energy and goodwill: "What you're getting now is officers who are just thinking, 'Stuff this – I'm just going to treat this as a job'," he says. "It's, 'I'm going to turn up, do what I've got to do to keep people off my back, and go home. Why should I put myself out?'"

Police officers converged on London in May 2012 to demonstrate their anger at government proposals. Photograph: Dan Kitwood/Getty Images Europe

At the Home Office, the response to all this is terse. "Our reforms are working and crime is falling. Policing continues to be a well-paid career that recognises the important job officers do and rewards their hard work and dedication." May's changes, the statement continues, "add up to the most radical overhaul to policing pay and conditions for 30 years", built on the idea that "we need to bring management practices into line with those elsewhere in the public sector and the wider economy".

The second half of my night in Bristol takes me to the city centre, in the company of three officers playing their part in a weekly ritual called Operation Brio. It begins with a briefing session involving 35 policemen and women and a run-down of likely trouble, all of which inevitably revolves around drink, and city-centre pubs, bars and clubs, which attract around 35,000 people on a Saturday night.

The next three hours start slowly, but they soon fall into a pattern. By 12.30am, the blue light atop the van is regularly flashing. Everything passes in a blur of petty violence, vomit and 60mph sprints to yet another incident. One rampaging twentysomething man throws another into a road chock-a-block with cars and taxis, and out come the handcuffs – only for it to be revealed that they are brothers-in-law. A hapless youth has been brutally punched and bloodied by a man who has been refused entry to a club, but seems much less concerned with what might have happened than the fact that he has mislaid his phone. Each flashpoint has its own cast: perpetrator, victim, well-meaning friends and rubbernecking passers-by, all of them drunk.

In the van is 35-year-old Sgt Caroline Froud, who has been a police officer for 14 years. Does she feel she is working even harder these days? "I would say so, yes," she says. She mentions the pressures on Avon and Somerset police that came from last year's Olympics, but also the reductions in police budgets, and how they have affected the team in which she works. "It's the numbers game. Up until April last year, we were two separate police stations and we both had an inspector, and each team had two sergeants. That's two inspectors and four sergeants, and there were a higher number of PCs. Now, we've lost an inspector, and a sergeant and a couple of other officers." She looks around to check that she hasn't said anything that will get her into trouble. The blue light flashes again, and off we go – into the wee hours, and more trouble.