OK
You have a green cylinder, which must be fed from a cold water tank higher in the house, most likely in the loft (unless you have a pump, which would be noisy)
Looking at the amount of black material, it seems to me to be too much, and the wrong texture, for a rubber tapwasher.
Unless it is attracted to a magnet, my best guess is that it is detritus from the loft tank, probably from something that has fallen in.
If you, or somebody braver, can get up there with a torch, a bucket, and a kitchen sieve, you can probably get it out.
If it is something undesirable, get somebody to turn on the COLD bathtap while you watch the loft tank. If the tap draws water from the tank, you will see the ballcock open and start to squirt water into it.
Come back and tell me if it does and I will advise further. Don't run the taps again until advised. Use the kitchen cold tap, which comes straight off the main and will be clean.
If you are lucky there might not be anything undesirable in there.
Keep the hot water cylinder hot (turn up the thermostat if you know how) because the heat pasteurises it and kills many bacteria.