Apparently not in our house Mr Athley says that the upstairs cold tap bath and basin are from the tank but the downstairs supply are from the mains water supply.
Well our downstairs water is clear whereas upstairs it is cloudy - aparantly it is fine to drink, wash teeth, bath etc however it is cloudy because of air in the pipes (quite an old house we live in!!) However we have had the odd drink from it but in general we use upstairs for washing issues and downstairs for drinking but it hasn't killed us yet.........
I think the theory is is that if your bathroom water is supplied by a tank rather than the mains it's not safe to drink as it could have anything in (dead flies etc) but I can't see it would be a big problem, as crosso says it's safe to brush your teeth with so it can't be that bad!
It's really strange that you asked this question tonight as I was reading about what is in tap water and why a lot of people filter it. This topic came up and as most people have already said previously, it depends if your cold water in your bathroom comes from a tank, if not then it is safe to drink.
If the cold supply in the bathroom is from the mains it is perfectly safe, if it is fed from a tank in the loft don't drink it, could have a dead mouse in it, or if you have had the plumber from hell in your loft,he might have had a pee in it, or worse !!!
I've always drunk water from the bathroom tap aswell as the kitchen one. I have no idea whether it's connected to the tank or not. It doesn't look any different and i'm still here!
There is a way to tell if your water is coming striaght from the mains supply or a tank (or so i've been told).
Turn on your cold tap and then put your finger underneath it to try to stop the flow. If the water is coming from the mains supply you should end up getting a shower! If it is coming from a tank then the supply should stop.
Sorry if anyone gets a soaking trying this and I must say that I haven't tried it myself as I know my bathroom water comes from the mains!!!