I have googled this and found a number of answers and videos which all say that this can be done by setting the brush size slider in the brushes panel or brush editor panel.
I'm either clicking on the wrong thing or doing something strange as I don't seem to have the same options available to me. At least setting all the sliders to their minimum value still leaves me with a 3 pixel wide square brush:
I'm using Gimp 2.8.4. I'm obviously making a basic error, can anyone help?
As of GIMP 2.8, the way to paint with a 1 pixel brush using the pencil tool is setting the brush size to "1" in the Pencil tool options, when painting, regardless of Brush's shape or native size.
In previous GIMP versions, the "pixel" Brush which was an image one pixel in size was available in the UI. It is currently hidden, and available only for scripts which happen to make use of it. The new way brush size works from the tool options make it obsolete.