In my kitchen, tucked away out of sight at the side of the washing
machine, there is a 3ft by 2ft patch of bare brick, no plaster.

* As a quick fix, will wallpaper stick to bare brick?

ha ha

* Failing this, would bog standard internal white emulsion be an
option?

Sure. It'll look like sh1t of course, much worse than bare brick, as
will all the options mentiond so far except plastering or PBing it.