Anyone can claim asylum
Whether that person qualifies as a refugee depends on the law in the country where they make the claim which usually involves an administrative decision making process. If a country is a signatory to the UN convention on refugees then local law will reflect that in some way. This outlines the process in australia.
Under the convention a refugee is a person who:
... owing to well‐founded fear of being persecuted for reasons of race, religion, nationality, membership of a particular social group or political opinion, is outside the country of his nationality and is unable or, owing to such fear, is unwilling to avail himself of the protection of that country; or who, not having a nationality and being outside the country of his former habitual residence as a result of such events, is unable or, owing to such fear, is unwilling to return to it ...
Being a citizen or a resident of a state with an authoritarian government does not, of itself, make one a refugee.
The individual must have a “well‐founded fear of being persecuted for reasons of race, religion, nationality, membership of a particular social group or political opinion.” Most citizens of most authoritarian countries are not persecuted or at risk of persecution.
They also must be outside their home country.
You can always emigrate
The UK has no general restrictions on people leaving the country in search of more freedom.
However, you need to choose carefully. At last count the UK is less authoritarian than 151 of the 167 countries in the world. If you are going to emigrate there are 15 places you could go that are better. Fortunately, 4 of them have English as a primary language and, not coincidentally, a system of government in the UK model.