You arrive back home from holiday late at night to find the house ransacked – your jewellery, the smart TV, the laptop all gone. You reach for the phone and dial not the 101 number that will connect you to the police but your local private security force. They reassure you they’ll have one of their officers over right away to take evidence and a detective around first thing.

It may sound dystopian. But with police forces under strain from cuts – police numbers are at their lowest levels since the early 1980s – there’s a growing business in private security. £200 a month will buy Kensington and Mayfair residents a subscription to My Local Bobby, a bobby-on-the-beat service with nationwide aspirations. In Frinton-on-Sea in Essex, 300 people pay £2 a week each for overnight patrols by a security company. And the creeping privatisation of once-public spaces such as shopping precincts and parks means private security guards are becoming a familiar sight in towns and cities; in 2015, there were 50% more security guards employed in the UK than police officers.

Policing is a non-negotiable responsibility of the state

I imagine that Sir Robert Peel –widely regarded as the founder of modern policing in Britain – might regard these developments as a backward step. It was thanks to Peel that, in the 19th century, policing became one of the first universal public services provided by the modern state.

But policing is being stretched like never before. It’s not just the cuts: investigating crime is becoming more complex and resource-intensive. The vast amounts of personal data we now amass have hugely expanded the amount of evidence the police have to work through on crimes spanning financial crime to sexual assault.

The conversation about what the police can and can’t do in constrained times was brought to a head last week by police chiefs Sara Thornton and Cressida Dick. The takeaway is that we can expect the police to prioritise violent crime over minor theft, drug dealing over dinner-party drug taking and the production of images of child abuse over their consumption online. The police are simply screening out some reports of crimes – almost half in one area of the country – because they don’t have the resources to follow up.

Rationing isn’t new; resources have never been infinite and when violent crime is rising – two London teenagers were fatally stabbed in separate incidents in 24 hours last week – the police have to prioritise. In an either/or dilemma, no one would argue that bike theft should take precedence over violent assault.

But we can’t pretend that the consequences are palatable. You don’t have to buy into the broken windows theory – the controversial idea that failing to police low-level disorder sends violent crime rates up – to see the problems with the police retracting. If there are no consequences for viewing images of child sex abuse online, it’s not inconceivable that, somehow, people will find a way to supply it.

When your property has been stolen and the police have told you they can’t look into it, your first thought isn’t: “I’m so relieved the police are prioritising violent crime!” You feel violated and that the state isn’t fulfilling its duty to you. And how many times does it take someone to feel that way before they take matters into their own hands?

That might be a service such as My Local Bobby, if you’ve got a spare couple of grand or so a year. Tony Nash, one of its founders, argues that it’s no different from buying health insurance. But people buying private health insurance is a problem: the more the affluent opt out of universal services, the more it eats away at the broad social consensus we should pay taxes to fund them and reduces the number of people invested in those services getting better.

With policing, there’s even more at stake. The rule of law depends on the police being there to serve all citizens equally. That’s not true of a private security guard or investigator. They’re there to get results for their clients, not serve the public. And while they don’t have full police powers, the company that runs My Local Bobby boasts of achieving more than 400 convictions through private prosecutions.

Think of the lack of trust some minority communities justifiably have in the police, then imagine how that gets magnified by private security firms for whom the public interest is a secondary concern, if one at all, and who are not subject to the transparency and complaints procedure you would expect from a public agency. Imagine the social division and resentment that would rightly follow.

It’s extraordinary we’re seeing an increase in private policing and vigilantism under a Conservative government

Those who can’t afford private policing might feel forced into vigilante justice if the police can’t investigate what they see as important. There’s some evidence it’s on the rise, particularly in relation to “paedophile hunters”: the proportion of court cases for the crime of meeting a child after sexual grooming using vigilante evidence rose from 11% in 2014 to 44% in 2016. Vigilante justice is no less troubling than private policing. The self-appointed crusaders have no way of judging someone’s guilt or innocence, but that doesn’t stop them meting out mob justice via social media, ruining people’s lives through public shaming.

There’s a reason why policing became a key function of the state long before health and education; why the need for a police force is even less politically contested than the need for the NHS. Policing is a non-negotiable responsibility of the state; without it, there’s no rule of law. It’s extraordinary we’re seeing an increase in private policing and vigilantism under a Conservative government. As much as my inner lefty hates to admit it, even a booming private health insurance industry would worry me less than a surge in My Local Bobby subscriptions.

• Sonia Sodha is chief leader writer at the Observer and deputy opinion editor at the Guardian