I am desperatley trying to avoid rotoscoping.
No way. In a world full of choices you made the worst thinkable decision of shooting it the way it is - low contrast, many similarly colored items, fine structures. And did I mention that the refractions from that glass lamp alone will add a level of complication? There simply is nothing here that would allow even the smartest automatic effect to detect anything and masking everything manually is pretty much the only way, which if little ginger head isn't moving around too much might not be that complicated, after all.
If I were assigned the task of fixing this project I'd stabilize (not warp stabilize) the shot to remove any camera movement using the stripe on the back wall as my target, then I'd bring a frame of that stripe into Photoshop and clone it out, then import the PSD and mask it so that most of the scene except for the stripe was showing through, then I'd reintroduce the camera motion and add it to the psd file, then I'd do my best a color correcting so that the wall appeared to be relatively white and the shot had some snap. There is no way I would try and bring the background to 100% white.
If you don't understand what I suggested let us know and we'll try and explain it to you.
There are lots of tutorials out there on removing unwanted things, like microphones that dip into a shot. It's the same technique. Fix the vertical stripe and you're 90% there for making the shot acceptable.
You are not going to avoid rotoscoping on that shot. Although, you might be able to use the Roto Brush along with the Refine Matte effect to make the job somewhat less painful. Make sure you go through these resources before trying to use it though: Roto Brush in After Effects - it's not as intuitive as it may look.