I got to pulling down some more wall today, trying to figure out where my nasty draft is coming in. It turned out to be a lot less ugly than I expected, although a decent fix is going to take some more demolition. For now I've stuffed fiberglass into the spaces it seems to be coming from, so hopefully that will solve the problem even if only temporarily. I'm not really wanting to gut the entire room just now, I just want to dismantle the absolute minimum so I can block the drafts and stop the relentless source of cold air.
It's supposed to be a bit warmer later in the week, so maybe I'll take the chance to fill a couple of holes in the exterior brickwork, drill another hole for a new cable to go through, run a cable that will ultimately power an outside light (and seal around it, to avoid letting cold air in!), and clean up a couple of other nasty bits on the outside brickwork. That will feel like at least something of an achievement.