I'm asking this because I heard two people say fink* instead of think & bof* instead of both: a non native university teacher of English and a native speaker of English. If it's not a speech impediment which variety of English does it belong to?
I think you are referring to the
it refers to the pronunciation of the English "th" as "f" or "v". When th-fronting is applied, /θ/ becomes /f/ (for example, three is pronounced as free) and /ð/ becomes /v/ (for example, bathe is pronounced as bave). Unlike the fronting of /θ/ to /f/, the fronting of /ð/ to /v/ doesn't occur in any dialect word-initially (for example, while bathe can be pronounced as bave, that is never pronounced as *vat).
Th-fronting is a prominent feature of several dialects of English, notably Cockney, Estuary English, some West Country dialects, Newfoundland English, African American Vernacular English, and Liberian English, as well as in many foreign accents (though the details differ among those accents).1