Yes anybody can take the UK amateur radio exams from any country. You can take the exams online and book the exams on the RSGB website. There are 3 levels of Licence, Foundation, Intermediate and Full.
If you are temporarily visiting the UK you may be able to operate in the UK using your existing Licence. CEPT T/R 61-01. For operating in the UK longer-term you may be able to show your existing amateur Licence to Ofcom to get a UK Licence. (It depends on what type of Licence you have).
Once you pass the UK Full exam you will be sent a HAREC certificate in the same envelope as the Full pass certificate. Someone with a HAREC should be able to get an amateur radio Licence in other participating countries. CEPT Recommendation T/R 61-02.
You do not need a UK address to take the UK exams. RSGB will happily send certificates abroad. If you want a UK callsign you will need a UK address. You don’t have to live at the address, and you don’t need to have any right to live in or even enter the UK. You do not need to get a UK callsign in order to get a HAREC certificate to obtain a licence abroad. It is sent in the same envelope as the Full pass certificate.
Booking your amateur radio exam
https://rsgb.org/main/clubs-training/for-students/paying-for-your-exam/
Licensing guidance document for amateur radio – Ofcom
https://www.ofcom.org.uk/siteassets/resources/documents/manage-your-licence/amateur/amateur_radio_licence_guidance_for_licensees.pdf?v=368087
CEPT T/R 61-01 Document
https://docdb.cept.org/download/2ae38a89-e58a/TR6101.pdf
CEPT T/R 61-02 Document
https://docdb.cept.org/download/2569