I agree with the purple rug ideas, but maybe something with a pattern? I like the mirrors idea too, especially if you want to keep it modern. But if you go for art- I wouldn't bother trying to hard to match it to the room- go for something you love. If it has a bit of purple or green or grey in it fine, but don't pick something just because it matches- I think it screams inpersonal.

Hi. i would look at something like farrow and ball old white shown here which would work with your tiles and choose a similar colour for blinds. the table and chairs are lovely but the contrast is quite strong, maybe consider adding a stoneware vase with some stems (also similar tothe pic below!) and maybe place on a woven mat. Maybe also a cushion for the sofa with a little red in the pattern?

I think its a question of scale. Your art is not large enough. Some shelves might give you some room for storage and a base to display some artwork. I wouldn't paint the wall. I would put up a couple of long shelves maybe 3 or 4 on the tv half of the room towards the corner. Floorlamps create lovely pools of light. Conside a side table with a lamp. We never use our ceiling spotlights although they are on a dimmer. Look at the space in the day and see where you need the light at night. Is there any furniture between the piano and the tv unit? You could also buy a narrow storage unit with glass shelves. The height of everything is too similar. Do a Houzz search for shelves and floorlamps and/or tablelamps in photo's. There are some lovely examples there.

It's great that you have cookery books and a love for plants - those are perfect starting points for adding character to the space. Besides standard shelving, consider mixing in some floating shelves to display your cookbooks and maybe a small indoor herb garden for your plants. You could also hang some framed food-inspired art or decorative plates to add a personal touch.