Does the term "criminal" imply conviction?

Note: I am writing this in England. Assume the legalese to have a British bias.

Does the term "Criminal" (def: 'a person who has committed a crime') imply that this person has been convicted of a crime or just that they have performed it?
Is "committed" a term of art in this instance – that is, does an action cross the line from "doing an illegal thing" to "committing a crime" only once it has been recognised by formal process?
Can someone who has performed an illegal act – whether or not any other person saw it or whether or not they were convicted, tried or punished for it – be classified as a "criminal" or is it a protected term?

As the question itself says, a criminal is, by definition, somebody who has committed a crime. So far as the rules of the language are concerned, the word can be correctly applied to anybody who satisfies that definition, i.e. to anybody who has actually committed a crime.

In particular settings, there may however, be further rules, i.e. the rules of something other than the language, that limit one's use of the word. In a legal setting, one thus wouldn't refer to somebody as a criminal if the person hasn't been convicted of a crime, but that's because of the legal principle (not a rule of the language) that, for the purposes of the law, everybody must be treated as innocent until proven guilty.

Similarly, as a matter of good journalistic practice, and to avoid the risk of being sued for defamation, one normally wouldn't refer to a specific person as a criminal in a newspaper article, if the person hasn't been convicted. Notice, though, that this doesn't preclude the word from being used in journalism for those who haven't been convicted, in general, i.e. when no identifiable person is referred to. For example, a journalist may, without contradiction, write something like 'Many of the criminals who commit such acts never get convicted'.

The Cambridge English dictionary online defines the word criminal as follows

Someone who commits a crime

Merriam Webster (admittedly US) online offers two definitions

1: one who has committed a crime 2: a person who has been convicted of a crime

Collins onine gives a similar but slightly different definition.

A criminal is a person who regularly commits crimes. And it gives this example "A group of gunmen attacked a prison and set free nine criminals in Moroto"

The point is that if someone commits a crime or commits frequent crimes, s/he is in fact and will continue to be a criminal, whether s/he has been convicted or not. Because of that, you can say in public that s/he is a criminal and what you say will be true.

BUT (and this is a big but) I would advise against saying in public that someone is a criminal, unless s/he has been convicted or a pretty sure you can prove it in court, because you could well be on the losing end of an expensive libel action.

Even then, there are exceptions to this. It is possible to use the term rhetorically. We can all think of politicians who have publicly claimed or suggested that a rival politician has committed a crime. Usually, the victim in such a political situation does not take legal action, but in theory they could, I imagine (I am no lawyer).

We can even say someone is 'a criminal' for doing something that is morally very bad but has not broken a law: sort of metaphorically.

There is nothing in the Lexico (UK Dictionary) definitions of criminal, crime, and commit that proscribes the common colloquial usages of these words.

criminal: A person who has committed a crime.

-- Committed does not imply convicted (of). That is, the definition doesn't say convicted of a crime -- the act in question could have merely been performed.

crime: An action or omission which constitutes an offence and is punishable by law.

-- An offence that is punishable by law does not imply an offense that was punished by law.

commit: Perpetrate or carry out (a mistake, crime, or immoral act)

In ordinary English language and usage, none of these words is a "term of art" or "protected". That could be (and probably is) the case if you focus solely on the legal realm and reference an authoritative legal dictionary, as suggested by @Greybeard.