The linguistic feature is known as th-fronting, where a dental fricative (both th-sounds) becomes a labiodental fricative (f,v) while the voicing remains the same. First noted in the late 18th c., it is now a common feature of several dialects of
English: Cockney, Essex dialect, Estuary English, some West Country and Yorkshire dialects, Newfoundland English, and African American Vernacular English. Most recently, it’s been attested in, of all places, Glasgow.
The feature is used to comic effect in Catherine Tate’s character Lauren Cooper and her catchphrase “Am I bovvered?” which during Comic Relief 2007 then-PM Tony Blair unleashed on Lauren instead. Blair doesn’t quite manage the pronunciation.
You can even buy the t-shirt: