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When you say external applications - just clarifying it's an internal wall on both sides. But this may be me being thick and not understanding what you mean.
I am wondering if it's condensation related. The room it is near suffers badly from it and I wonder if there just hasn't been enough ventilation in the past. We've got someone at last installing a proper extraction thing there next month. I'll continue scraping away today (though am unsure whether to take back the entire wall or just the affected area. The section currently painted on the left for example feels totally different to the touch/sound (it seems fine).
CYOA-
When you say external applications
Render / paint etc... not so relevant in your case.
In general, though, for old lime mortar solid walls, anything other than lime can be problematic where water / moisture / damp is involved - Things that keep water out tend to also keep water in even more effectively (and while they may work perfectly when they are first applied, over time they will degrade and let water in).
If you go back to porous lime (which is what that gravelly filler crap looks like) it would be able to dry out. When you have the extraction in, and wait for a month or two over winter, you can see if that's the proximate cause if it dries out.
Unfortunately, a lot of fixing problems involve "try this one thing. wait a long time. didn't work? try something else".
NotThamesWater
This, mostly.
Strip back to brick and leave for a while.
Then you can see what the problem actually is (without moisture wicking around because of the mix of porous and non-porous, modern and old materials).
Using pva / creams / modern fillers on your side will mask the problem for a while (even years), but ultimately make it worse as it leads to damage of the bricks & mortar.
Otherwise, mostly what @JonoMarshall says.
As far as external applications, I'd want to avoid anything that wasn't lime based.