No. It's not obvious. How to turn the faucet is on is obvious. How to get yourself clean without burning or freezing yourself is not.
Like Belita, my face breaks out if I reuse the water. I need to wash in running water.
I have used the running hands back and forth under the two taps method, but you can burn yourself that way if the hot water tap gets too hot. I've burnt myself when I didn't wait long enough after flushing the toilet or let the hot water tap run too long. Most Americans are used to being able to adjust the water temperature before they touch the water.
I also feel that this method doesn't get me as clean as if I had mixer taps because with mixer taps I can cup the medium-temperature water in my hand and spread it all over my face, whereas with separate taps I have to quickly splash the running water from the tap onto my face because I can't leave it on my hands too long or it will freeze or burn me so I don't rinse my face as well.
In fact, when I used to wash my face in the States, I would wash with warm (not hot water) to open my pores to let the oil and dirt out, then rinse with cool (not cold) water to tighten my pores. That kind of temperature adjustment isn't possible with separate taps.
I am used to non-mixer taps now and wouldn't be posting if someone else hadn't, but I can see how someone could have difficulty with them, particularly someone new to the UK.
Paul, I have also read on this board about there being non-mixer taps in New York City, but I have never seen them, not even in Greenwich Village, which is probably one of the oldest parts of the city. I assume they are in some very old homes/apartments; they are no the norm.