Is the draft coming through the windows, or around the window frame.
If it is the windows, get the landlord to fix it, it will be his problem.
If it is around the frame, it may be an argument as to who's responsibility it is, but that is still something you don't get involved with, it's between the landlord and the management company.
Either way, shout at the landlord.
FYI, if it is around the window frame, this would suggest really poor fitting, and raises the question about lack of expanding foam or cavity closers around the window (which should be present).
I think it's the window rather than the frame, I will get touch. At the moment it's only got a blind, I will take a photo to show you what I mean