Just came across an essay I read years ago as a student, about how Björk's accent and phonology change based on whether she is or is not heavily identifying with Iceland at a particular moment. It's a kind of code switching.

To summarize: She has a very heavy Icelandic accent (for which she is known) primarily when talking/singing about Iceland, or associating with it. Other times, she has a noticeable Estuary (London) English accent, mainly when addressing or associating with English audiences.

The full text can be found here, if you're interested:

https://skemman.is/bitstream/1946/11558/3/J%C3%B3n%20Fri%C3%B0rik%20J%C3%B3natanson-1.pdf