@Failingatthemoment we had the same issue in our 400 year old house, mainly because the previous owners had added an extension leaving an internal window (originally external) between it and the adjoining room.
As others have suggested and because we like darker colours anyway, we decided to embrace the dark - you actually couldn't sit in there during the daytime without putting lights on - with olive walls and loads of books. As we both hate overhead lights in living rooms we had several table and floor lamps in there plus four mirrors but it still wasn't a pleasant place to sit during the day, so I avoided it for four years - it certainly wasn't a pleasant place to sit with a book!
We contemplated the extreme step of removing the extension altogether but didn't want to devalue the house by reducing its size. We looked at sun tunnels - another option for you perhaps? - and adding veluxes to the roof of the single storey extension to throw light back into the adjoining room, but didn't think any of these would make enough difference for us.
It was always on the agenda to replace the horrible windows on the extension frontage but we made the decision to open up the two spaces by removing the internal window (and adjacent French doors) - and adding structural beams obviously - which immediately helped. We then took out the whole frontage of the extension and built floor to ceiling windows that let in tons of light (south west facing).
It's made a massive difference and whilst what is now the 'dining end' will never be in-your-face bright, we have a lovely light filled living room and don't need lights on during the day now! We saved loads of £££ by building the whole lot ourselves as thousands for new oak DG windows wasn't in our budget.
Sorry, not much help, I know, but wanted to share my experience with you. Really hope you find a solution to your problem as I know how depressing dark rooms can be!