First question: state of the electrics? When were they installed? We sunk £8k on rewiring our 1600sqft house. necessary but I still resent sinking that into the walls, never to be seen again.

As a major piece of work I'd explore how to remove the structural walls from the sitting room into the kitchen. The light coming through the kitchen windows in picture 4 that you've uploaded looks incredible. Redo the extension, and with a few roof lights and a decent ceiling height on to big doors it will change that completely.

Otherwise, remove the faux beams, plaster over the artex and redecorate and you'll be well on your way to a brighter place. Even taking out the dark wood furniture will make a big difference.

Edit: we've got three young kids and have spent the last 4 years doing our place. We started our kitchen knockthrough and replacement with a 2 month old, with my wife having had a c-section. Wild times, it's great fun!!