Moving To Different Bedroom In Annex/extension?

there is one problem, however, which is that the bedroom I will be moving into is part of the house extension. The biggest problem with this is that my gaming PC uses powerline adapters to connect from my BT HomeHub 3.0 router to my PC currently upstairs (in the bedroom I share with my brother) and the house electrics are all fine giving me full speeds. But when I tested the powerline adapter in the extension, I got no connection upstairs (in the new bedroom) and a very weak connection downstairs (in the annex). The annex's electrics are only really an extension of the main box although they are part of the same network but perhaps not a complete circuit... or something rather...WiFi signals do get to the annex bedroom ok although I'm not a fan of using WiFi and the signal quality received from a laptop's WiFi card is not fantastic.

-The BT HomeHub 3.0 can't be replaced with something else

-Drilling through walls is a rather unlikely to be approved by my parents

-Routing an ethernet cable through the house, although probably the best option, is also quite hard to achieve without making holes in things.

-There are no vents in either the room where the router is (attatched to master phone socket) or in the annex bedroom.

I have had a few ideas myself which range from getting an dual band high speed WiFi adapter to install into the PC to routing the cable outside, although the route I was thinking of would probably risk me breaking my neck and certain windows would have to be open all the time to fit the wire through.There are no vents in either the room where the router is (attatched to master phone socket) or in the annex bedroom.