When we had a similarly laid out room we put a (huge, 9' long) mirror on the wall opposite the windows to bounce additional light around. However, our room overlooked our very rural deep front garden, with no passers-by able to see in as the room/garden were above street level, so I can see why it may not be such a good idea in your situation @Kitchenbattle.
I'm with you on not wanting to wall mount the TV as I'm not a fan of that. Yours does seem a bit low, ours is on a vintage sideboard which is the perfect height for viewing. There are online guides which help with positioning TVs for optimal viewing and I researched this thoroughly before committing to purchasing the sideboard!
An area rug will look great once you manage to find something you love - it takes time if you're not prepared to settle for something as a space filler. I looked for ages for most of ours - apart from a splurge at Liberty with an inheritance, the best ones I've found have been antique/vintage ones on eBay. Dunelm is a good shout though, but I'd be prepared to wait for the right one.
Art, books, more lamps etc will soften and personalise the space. I agree with regards to the overhead light - we rarely use ours (except in the kitchen and bathroom/cloaks), preferring lots of lamps, but a statement light fitting (which could be on a dimmer) looks far better than a shade in most situations, imo.
Overall, if it was my room, I'd want to inject more colour, but specifically more pattern into your lovely room as at the moment that seems to be what's missing.