Condensation and salts question

[Trinity89]

Evening people, hoping for some advice and opion on how best to proceed. Our utility is the coldest room in the house, presume it was a converted out building long before we moved in. In the summer we had a window bricked upto so we could put storage in. Due to the cold weather the metal trim under the plaster has become so cold you can see its outline and the wall above it was damp to the touch, cold wall meets warm wall on the other side. There is a small w/c with a fan and radiator joining onto this and room, the door to the wc was mostly kept closed which i dont think helped, its now open and the wall is no longer wet. My query how can i prevent it happening next winter, my wife wants to tile the room but im not sure.

The last pic is a window in a bedroom directly above this door frame, the ceiling void in this utility joins onto this room and there is a cold spot under the window, this was also wet to touch. It took me a while to get to grips with the condensation but it is now kept it to a minimum. I presume its salts on the window frame as i wiped it away and its came strait back and its not damp to the touch and it only appeared when the cold weathwr started. I use a demudifier and put a pot of salt on the window sill to soak the moisture up .Ive also got someone coming to look at the guttering as it has been leaking abovw this window but there is wet patches so dont think its a leak. wondered how best to proceed really. Thanks in advance

 

[foxhole]

Was the wall the door frame sits in the original exterior wall ?

 

[Trinity89]

As far as I know yes, it's never done it before but I can't recall it been so cold for so long since we've been in the house

 

[foxhole]

If the extension roof to rear wall was not finished correctly rain hitting the rear simply falls thru the wall past the roof and emerges at ground level .