First off , its very difficult to answer stuff like this without seeing the wall but we can have a go at what we think you might be trying to explain. So , the paint was blubing and underneath if looks like sand (assuming down to the brick) . It does sound like damp plaster. However ,the plaster when this house was built was actually a mix of sand and lime mixed with horse hair. So the sand like substance may well be this. Sand and lime does withstands damp very well but 100 years later , it can perish become 'sandy' and fall out . This type of plaster was up until 1952 the norm . After this new plasters were produced and were lighter than the old sand and lime , and given the name , Patent lightweight plasters. The most commonof these is Browning and bonding plaster but plaster board can be inculded in this as well. I'll come back to the replastering but on no accopunt should you use a lightweigh plaster to repair these walls. The way it is made means its always trying to always reconsitute itself and therefore not only useless on an old damp wall but will in fact suck the dampness out the wall .
Back to the damp. I do a lot of old properties , mainly terraces and flats . There are in fact still two thirds of all the housing stock in the uk. The rear of these nearly always suffer from dampness caused by a a few thing and usually a combination of them. Its easy to try and attribute the damp to one factor and that may well be so, but 'usually' its a combination . These are rising damp , penetratng damp (often from solid walls ) and condensation. You are right to mention condensation and this is often the triple whammy here. The rear walls are cold , they are a bit damp and then we have double glazed windows and doors and no where for all the cooking , showering and even breathing moisture to go . Extrator fans are helpful as are open windows (infact they are more helpful) but the condensaton often over whelms this or they simply aren't used. So all this condensation is a bit like filling a kettle up every day and thowing it on the walls. Eventually the plaster , if it hasn't already perished , does so now. This is my guess what is happening .
My view on how to deal with this and something we have been very succesful at , is not to use a solid plaster on the walls but to strip them entirly back to the brick , inject a dpc and mechanically fix thermaline boards to the walls. These are an insulated board with a plaster board bonded to them. This will provide a barrier to the penetrating damp (although its also important to make sure the outside wall is well pointed and in good condition and no gutters or downpipes are leaking on to it ) , a barrier to rising damp and a much warmer wall to help with condensation . Thats not to say you can forget about the condensation , it stil requires control.
Phil