As long as it's inside your boundary, I wouldn't give it another thought. You have been entirely reasonable in softening the effect with climbers which, as you say, will have no aesthetic benefit to you. We had a two and eight without our previous neighbour, who was a bloody nuiscance anyway, about a single skin wall they built between the two houses. The problem was that they refused to point it properly on our side and we were left looking at a dog's breakfast. The council said they didn't need planning consent for it, because although it was higher than permitted on our side, it wasn't on theirs, and that, basically there wasn't a lot we could do, as they refused to either point it, let us point it, render it or do anything else with it. In the end we erected trellising that wasn't actually attached to the wall and grew screening plants. Get on and put up your shed. You can get some lovely colours in shed paint these days too that will make it easier on the eye.