I find myself copying the singer of the song's style and accent. My own voice is an amalgam of dialect because my mother was scotish and my father yorkshire, and I don't feel I have a local accent. I suppose many of us have mongrel voices, and we copy what we hear and like. However I think that's all for the good although it doesnt lend itself to a defining British accent. All our accents are evolving. Most of us will have been influenced by TV and radio pronunciations, as well as the singers we most like.
ps. I cant sing Geordie, the rest I make an attempt at initially, and it takes some time to find a way of bending it to my own inner voice.