Is the wall damp? Have you noticed any damp in the flat?
I'm hoping you will have luck with your landlord.
But, if your landlord is reluctant or unwilling to do anything, definitely contact your council's Environmental Health team (your council may have a different name for this function, so you may have to dig a bit on the website to figure out who to contact). They can evaluate the problem, and from what I understand, can force your landlord to make improvements/repairs if they deem them necessary.
When we called them them, they said to have our landlord's number ready when they came by. We ended up not having them come, since the leak was located and fixed soon after we contacted them, but they were very responsive when we did call.
We are also in a private rental, by the way. Of course, the downside with a private rental is that your landlord may prefer to terminate the lease, I suppose, rather than do anything.