Why do people with a British accent sing in an American accent?

I guess in general yes, people who sing in English tend to assume what would be described as an American accent. Although, I don't think it is completely American - more a sort of generic accent that you can achieve easily with singing. I think that would be the reason 'why' - it is easier to do. If you have a distinct accent, you'll notice that singing in it is relatively hard to do without falling into using this generic accent.

I'm saying 'generic accent' because I don't think it's American. I would have a very hard time saying where someone singing in English (whether native or not) came from based on their accent in the song.

It is still an over-generalisation though, and I know many artists who sing with their regional accent. Sometimes appealing to my ear (e.g. Biffy Clyro), sometimes not (e.g. Lilly Allen).