have a look at it - does the wall feel wet after its stopped raining for a few hours? is there actual water behind the paint? is the paint starting to bubble up because the water behind it cant escape? You might have an issue that its not just the paint that is causing the issue, looks like some of that wall has been repointed. If the house is old and they have used a cement mortar instead of an lime mortar that will also trap the moisture in the brick work.
Are you 100% sure you dont have a water leak somewhere in the house? Next time you go out turn off all the taps in house so nothing can use water. Check the meter and see what the numbers are, then when you return say 3 hours later check them again, this should tell you if you potentially have a hidden leak somewhere in the house.