Home Improvement

Perhaps not the same but I own a 150 year old home in America and I had foam insulation blown in. The insulation it provided was minor but what it helped tremendously with was drafts and air exchange. On older homes air leaks and sealing any cracks and drafts can potentially save you more money than adding actual insulation depending on how leaky it is. Food for thought though it might not help you.

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

Cork insulation would usually be skimmed over with plaster. You could have a look at insulatiing plaster too, but I think that needs to be thicker than cork to work well. Less munchable by critters though.

In an old building, you need to use breathable insulation, breathable plaster, and breathable paint (and breathable mortar, if you're repointing the outside). The moisture needs an escape route.

It might be helpful to know what kind of walls you have. What is the material, do they have space that can be filled with insulation material?