I love all the ideas already mentioned.
I'd definitely take the fabric down, remove the wallpaper and repaint that long wall. At least it's only one area
. I think you're on the right track with the colour, but paler. I'd also be tempted to paint the wall behind the door (adjacent to the drawers) the same shade, but you can judge better once the long wall is transformed! That should make a big difference instantly.
I like the idea putting the sofa against the current tv wall, to face the (old) fabric wall. Would this work? You could then put some chunky frames or canvases above it (the plasterboard should support? Google for advice!).
Can you lightly sand and satin gloss the door in white? I know that would bug me every time I looked at it and it's a relatively quick job (just keep the dog and toddler contained!) Add a new handle if the existing one is dated. If you want to change the style of door I'm sure it can't be too hard, I'm intrigued to find out in a minute. Is the current one really plain/ ugly and not worth rejuvenating?
Love the idea of a new white globe lampshade and rubbing down and repainting the table (white). I'm not sure there's space for it on the tv wall if the sofa is going there, maybe against the newly painted wall, opposite the door. Top with a plant, framed photo and table lamp 
If that looks odd then keep it at the kitchen end, just add a tablecloth (oilcloth? pale green/pink?) if you don't get around to painting it. I think Dunelm have a selection or you can buy it off the roll in the fabric dept.
I don't know if they're considered naff but I love having a small nest of tables (contemporary) at the end of the sofa. Somewhere to put your drink and useful to get out for visitors and children. I prefer these to a large coffee table (aka dumping ground) in compact lounges.
Agree with extra lamps (even just one table lamp and one floor lamp) to tie in and create cosiness, large patterned rug (hides marks better), curtains, large clock behind the door (I like the Ikea Skovel in two sizes/ colours. I saw similar in Asda the other week).
PP mentioned moving the tv to the newly painted wall and possibly a new white tv stand. Or paint the existing one?
Is there a substantial gap remaining between the (new) tv position and the window? Would there be space for the table (mentioned above) with a large framed mirror above it? Worth checking eBay ('local collection only') for mirrors, I've had some absolute bargains.
I'd be tempted to paint the drawer fronts (or even the whole unit) but I'm not sure what colour? Pale pink? Something else?? I'm not keen on the expanse of white at that end of the room but it might be improved when the door is freshened up and the wall behind the door painted pale green to break it up a bit. Add some two-tone curtains to tie in with the rug?
It seems a shame to waste the fabric from the wall. Maybe sofa covers are the way to go, or spare decorative cushion covers. Could you use it elsewhere in the house for curtains or soft furnishings (!)
You'll have to post some updated photos 