Gary -
You mentioned that the darkroom space was "adjacent" to this room, 3-4 meters away, but you didn't specifically say that the darkroom was behind the wall we see in the picture. One of the challenges may be in running the pipes from the sink area of the darkroom to this point to connect into the existing plumbing. That doesn't mean an insurmountable problem - just one more challenge to complicate things. Projects are never as simple as they first seem - - -
My inclination would be to view this as a DIY project rather than hiring a plumber. Based on what I see in the picture, the challenges will include tapping into the soldered copper hot and cold supply lines. That's not difficult, but if you've never tried soldering copper pipes, I suggest asking a friend to help/supervise. Frankly, my inclination would be to solder in a copper tap and nipple, and immediately transition to whatever form of plastic is readily available at your home center - that will make the job much easier.
It doesn't seem to me that the waste line will be much of a challenge at all. You can either unscrew the reducer fitting that the washing machine drains into, and replace it with what we refer to as a "Y-fitting" in the US (perhaps this is what Dave calls a "swept T", or else you can put a "y" in the washing machine drain itself to provide a spot to attach the drain line from the darkroom. Since that is all plastic, the work would be fairly simple. Again, if you haven't done it before, ask around to see if any of your friends are willing to help. I think I would be inclined to put a "check valve" in the darkroom drain line to prevent a problem the darkroom if there is a backup in the waste system.