Leak on 1st floor inside wall

[liz45red]

Hi

When there is a heavy rain over a period of several hours i get water dripping through about 1/4 way down on the inside of a wall and the wall feels damp. This wall is the link between myself and semi next door and is adjacent to the exterior wall. There are no marks or drips from the ceiling so i am not convinced it is coming from the roof. Is it possible it could be coming sideways from the exterior wall and finding a way through to the other wall?

I want to let this property out in a few weeks and want to sort this out and get the room decorated. This area will be behind a wardrobe so won't be visible but obviously does need doing and frankly can't get a builder to look at it for love nor money so wondered if there is anything i can do even if a quick fix myself.