You could put lining paper over the cork, so you have a paintable surface.
My flat has plaster render over brick for internal walls (external walls are lath & plaster).
My hallway has a styrofoam backed wallpaper. It gets damaged SO easily, and I haven’t found a decent way to repair it. I presume at some point, I just need to repaper it.
I think cork is a bit hardier than styrofoam, but just a heads up for high traffic areas