A foreigner's question on British pronunciation

Hello.
I've heard (say, in some British songs) the following pronunciation: the vowel in "got" was pronounced in a sort of American manner, more like in "but", for example. That was Blur, by the way. The sound was not even short, it lasted for some time (because it's a song).

It's interesting, how you (the British) feel it. Is it felt to be something alien or just one of the British accents? Also, I didn't notice any other occurence of such pronunciation with any other words where a similar thing could happen, say "pot", "stop", etc. I mean I didn't notice it in Blur's singer's speech/singing.

Thank you