In the UK the kitchen tap/faucet is attached directly to the incoming water main pipe.

The bathroom sinks, particularly in older houses, was sent through a header tank, so that the cold tap had a similar pressure and/or flow rate to the hot tap/faucet which was also regulated by a header tank.

Sometimes if not properly covered, those tanks were home to dead pigeons or squirrels, so you never drank from anywhere but the kitchen tap.

Might that explain the taste at your house?

Seeing if the water comes out at the same rate as the kitchen tap would be a good first test to see how it might be plumbed.