I used to live round the corner from a strange little place that sold cassette tapes (what we used for music and sometimes even data before CDs, for those too young to know). Everyone was convinced it was a front but it turned out it was a world famous tape supplier. Just happened to be based in my quiet little back street.
The newsagents next door to my last place have to have been a front though. Shelves were half bare, only ever stocked with stuff that doesn't go off. Always two or three guys hanging out in the back room, looking slightly surprised if you wanted to buy something. Cash only, no cards (not that unusual round here but they usually have a minimum purchase rather than just no card machine at all these days).
They were absolute sweethearts. Took loads of deliveries for us, always really nice about it. And that's more evidence that it's a front. Proper criminals are the best neighbours anyone could ask for because the last thing they want is complaints bringing the police to their door.
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.