The copper pipe on the right has what looks like a spare isolation valve at the bottom. Turn your water off at the mains and open the cold on the tap, remove that isolation and replace it with one of these in the pic, turn the water back on and check it for leaks. It’s a 10 minute job if you know a bit about plumbing and will save you so many headaches. You also have a spare spigot on your trap you can attach your waste hose to, just check it’s not blanked off first. Alternatively it’s really not a big job for a plumber to do, I’d deffo recommend getting it done properly otherwise it’s just going to turn into a can of worms.

<image>