Higher levels of metals can be introduced into water through your internal pipework and can cause a metallic or bitter taste.
This is most apparent after water has been standing in pipework for a period of time, such as overnight. You may also notice it in places where there are long runs of pipework or in places where water becomes warm as it passes to a drinking water point.
Try running water through the tap to clear any which has been allowed to stand. If you collect this in a bowl it can be used for watering plants rather than being wasted.
If you have new pipework the taste should improve with time as a thin protective layer of limescale will form on the inside of the pipework. Where water heats up during transit you should check the route of the pipework and the proximity of cold and hot water pipes. Affected pipework should be lagged or re-routed as necessary.
Occasionally glasses or cups that have been through a dishwasher may retain traces of detergents.
As a test, try rinsing the glass or cup with tap water and see whether the taste is still there. If so, adjust the settings on your dishwasher and use no more than the recommended amount of detergent and rinse aid.
If you've tried this but are still concerned, or you'd like more advice you should contact your water supplier.