I get influenced by stuff that isn't even music.
I'm conscious enough that how I'm singing is not my own accent.
For me, hearing the term 'apply yourself' was like a crucifix to Bella Lugosi's Dracula. 'Ahhh, it burns!'
If I sang the way I talk it would sound like "Tommy Steele sings Muddy Waters!"
If you are approaching the music with more reverence than the original guys invested into it, you are effectively doing it a disservice.
Because I'm English, I try not to make any purely American references, because I want to limit how much I'm pretending to be American.