Can my neighbour put their shed this close?

Got to our holiday let yesterday and found the neighbours have put a shed up in place of an old fir tree that was almost dead.

Their house and garden sits about 4 feet higher than ours and the wall between us I think is jointly owned.
No problem with them putting a shed there, despite it looking pretty ugly sticking up above the wall and blighting our view or the sky, however they’ve sat the thing right up against the wall and have even cut the soffit to facilitate getting it even closer to the wall. The roof edge is over the wall so rain water will discharge onto the top of the wall and down our side!

We I put our shed in, I made sure there was a 4 or 5 inch air gap behind our shed (the cream one with the sloping red roof) and that the roof takes the water away from the wall rather than onto it.

I don’t want to start a ruck with the neighbours, who we rarely see as both houses are holiday lets, but I’d like to ask them to move their shed over about 4 to 6 inches so the wall doesn’t start having moisture issues and their rain water isn’t discharging down our side of the wall.

Does anyone know if this is fair and legal request, or should I just suck it up and forget about it?