This is most likely to be particles of calcium carbonate which is found in higher concentrations in hard water. As hard water is higher in naturally occurring minerals it can cause taps to become clogged more easily.
Further information on hard water can be found here.
You should periodically clean the filter from your taps to ensure you’re getting the best quality water. You may still see these particles in your water, but you should not worry. Hard water is perfectly safe to drink, in fact there is lots of evidence that it can even be good for our health.
Black particles in your water may be due to naturally occurring manganese being disturbed following an issue such as a burst water main, or due to it staining limescale within your pipework. Your water should return to normal within a few hours of any disturbance.
Black particles may also be due to a degrading carbon filter on your tap or water jug or a broken washer in your tap. Black particles may affect the taste of your water but are not harmful.
Your water softener, if faulty, can release orange resin particles into your water supply.
Please contact an approved plumber to fix or replace your water softener (www.watersafe.co.uk). Water softeners typically need to be replaced after 10-20 years.