Has anybody done this, or can any architects/ building control people help?

My bedroom window is annoying me. i need to make it more soundproof. My building is listed, and the window is one of those historic types that you push up vertically to open.

What are your experiences with getting permission for secondary or double glazing on these kind of gaffs? It is ONE WINDOW. And because I'm on the top floor, you can barely see it from street level.