Maybe I can add something of interest and help here:
Usually I don't have such a voice in the back of my head. Maybe I used to, but I can't remember.
But -- the last year was very painful for me because I was in depression mode almost all the time. And when I was feeling depressed, there it was, that nasty little voice saying bad things about everyone and everything, constantly trying to make you feel worse.
I managed to get rid of it (and the depressive life period) by first consciously noticing and then understanding the voice. To notice it, calm your mind and notice what is left if you don't think consciously (mentioning this for the sake of completeness). Then to understand it, I needed to realize that in every human there is the deeply rooted need to feel bad once in a while. Eckhart Tolle describes it as your "pain body". It needs to be fed with negative thoughts, words and emotions regularly. And the negative voice in the back of our heads is doing just that.
So: Notice the voice, realize why it is there and what it is trying to accomplish, decide whether you want to feel bad or good. The last step will usually take some time to accomplish, but after a while of noticing and understanding it will get easier and easier. Until, as someone here said, you will be able to say "Thank you for your kindness, Mr. Nasty Voice, but save your breath, I'm fine."
