If you go follow to the  footnote from your link, you get:
Freedom of movement within a country encompasses both the right to travel freely within the territory of the State and the right to relocate oneself and to choose one's place of residence"
within a country and how it talks about
the State and not
Basically, it means that you can:
move anywhere in your country (for example, you are not forced to live near a farming field so you are left with no recourse but to farm that land for the landlord1).
move to another country that accepts you with the security that your own country will not deny you the possibility of travel.
move back to the country you are a citizen of whenever you want.
It does not mean that other countries have any obligation at all of accepting you2 if they do not want to.
In fact, the Wikipedia article explains all of that in a rather clear way in its very first section.
About the Theresa May article, it does not mean what you say.
Once the UK exits the EU, all of the EU nationals residing in the UK will no longer have the automatic right of residence/work in the UK, as EU treaty obligations will no longer apply.
May declaration means that she is planning to negotiate that EU citizens residing in the UK will keep its residence/work rights if the EU also keeps the residence/work rights of UK residents in the EU. But that she wants such a deal to include only EU citizens living the UK before article 50 is triggered, and not those that arrive later.
As happened with serfs.
2 Asylum seekers and refugees are covered by other international laws.