This is like when old people claim that Person X is not poor because they have a smartphone.
They still think about smartphones as a luxury item and do not understand that in Lambeth London you can't even register a birth and get a birth certificate without a smartphone.
The issue is not isolated to kleptocracies, many western countries are backsliding.
UK government has insane libel laws, they allowed the head of notorious Wagner group to sue UK journalist for libel in Britain. At the time head of Wagner was under international sanctions for war crimes. The journalist was reposting on the very same war crimes.
He was taking advantage of the same laws that protect extremely wealthy people in Britain, whether domestic or foreign.
Freedom of press needs investigative reporting, serious institutions to do research, etc. Without them, all you have is crazy people spreading conspiracy theories on social media.
Governments and people of power are attempting to surpress free speech as hard as ever today in most of the world, including your example Britain, or why not Australia or Brazil. The difference is that with the internet, speech is much more free _as practiced_ than ever before.
Your talk of "crazy conspiracy theorists" doesn't reflect well on the rest of your comment. This is a term that has been used very much as a slur to oppress free speech. It's basically the modern equivalent of calling somebody a heretic. Many of the people doing the investigative reporting you're calling for have to endure being called this when people do not agree with their reporting.
It's called "the press" because of the printing press. Could you think of some single individuals who have had massive impact on their societies by expressing themselves through printing pamphlets and books?
To make an analogy: A musician is no less of an artist because he or she performs as a solo act, rather than as part of a band.
Yet what "the press" means is "the body of news and journalism organisations". It is very possible to have a heavily constrained press, while individuals who are not the press and not part of the press have much more freedom to say what they like into the aether.
Here is what the Swedish National Archive writes on the subject, and I share the same view:
"When freedom of the press was introduced in 1766, many people wanted to express their opinions and spread their ideas. At this time, it was through shorter publications that people could communicate and reach many readers. A flood of printed material emerged, completely uncensored."
Some printers started to print the minutes of the courts to distribute them to the public. This way, people could read and see for themselves how the country was run and information could be disseminated in a completely different way than before. This became a profitable business idea. Freedom of the press and the principle of public access became a weapon for ordinary people against those in power and their decisions."
Not under the common definition of the press. By all means have a different definition, but if you do, it's only fair that you state up front that you mean something other than the common definition.
I think a more expansive view would ask the question of whether our discourse is improved at all, particularly political discourse.