This area is well shaded already and a dark colour on the walls and floor would suck the light out further. The rendering effect looks rustic rather than a crisp finish (unless there is another coat to go on yet) so not painting makes it look unfinished. I fess up I think grey is over used, there are plenty of other neutral colours out there so suggest Dulux limed white (note the actual chip is a warmer light taupe the website shows it as grey, duh!) for the walls. This will still be a nice contrast against the window frames and compliment the darker slate tile you want for the patio. You appear to have plenty of greenery and you could add a pop of contrast colour with a large pot (red, purple?). All the best with your project.

they are listed at the end of the article as timber look tiles floor tiles World of Tiles -TIMMAR 159M - timber look porcelain tiles

We just did a similar thing in our house. We had the orangeish timber skirting, doors and architraves. The walls were a very light beige. All the timber we painted white (dulux lexicon quarter), and went with a lovely grey on the walls (Taubmans zurich white). I was very happy with the white trim, I thnk if we had left it the house would still look dated. I've attached some before and after (sorry for low quality and different angles, they were just quick snaps with my phone).

You could zone the two areas by the use of rugs, additional lighting, and in the way you group and arrange furniture. In addition to the shelves, you could consider a pendant light over the bench, and once you decide where your dining set will go, another larger, different pendant above it, but suspended lower. Depending on your style, you might have a round sisal rug or runner in the kitchen, and a large woven rug in neutral tones under your dining set (for example).