Define "the government"...
All utilities have been privatised for a considerable time. Prisons are run by private companies. Likewise construction, so-called "public" transport and refuse disposal. Schools have had substantial elements of privatisation. Various elements of the NHS have private competition, and some (e.g. dentists, opticians, even GPs) are entirely privatised already.
How successful these have been is very questionable. Let's just say that for many of these privatised services, it costs the government more (in real terms) than those services cost when they were publicly-owned, and the quality of service is not necessarily better. Still, belief in the unequivocal benefits of privatisation is a near-religious conviction without evidence, not an evidence-based policy, and it's not possible to argue with a belief that doesn't have evidence. This means that any attempt to discusss this will simply be dismissed out of hand by its advocates.
The last 30 years have also proven that the general public are perfectly willing to accept privatisation as a way of delivering public services if the privatisation advocates tell them that it will deliver those services better and cheaper. It's also proven that the general public will then tolerate the situation later when it turns out that privatisation delivers worse, more expensive public services. The failure can be easily blamed on the individual companies delivering those services, not on the systemic failure of the policy.
So, how to deliver your dystopian vision? The first simple steps are to privatise policing and the judiciary. Policing is easy - we already have private police forces running prisons, transporting prisoners and providing security for various public places, after all. For the judiciary, it could be as simple as professionalising the role of judge/magistrate.
Once you've got that, you're mostly set. You do have the question of where the House of Commons, the House of Lords and the Queen would feature in accepting this, though. The Commons could fairly well be rigged, but the Lords would be much harder. Even though the Lords don't have the power they used to, they can still call the Commons on doing unethical stuff (after all, that's their reason for existing). It's not the same as a veto, but it can expose the situation to the public.
And the Queen would also be involved, since in theory she runs the country. As a constitutional monarchy, for her to get involved would be pretty much a nuclear option which might take the monarchy down if she didn't have the support of the public, but if the result would be bad enough for the country then it's perfectly imaginable that she would effectively lead a coup. So you need a monarch prepared to let this happen on their watch too. It seems unlikely that Liz 2, Chas 3 or Bill 4 would allow it to happen, but we've had enough bad, cowardly or ineffectual monarchs that you can't discount it completely.