There are actually three varieties:
- Mixer tap, with one handle
- Mixer tap, with separate hot and cold handles
- Two completely separate taps, such that the hot and cold water only mix in the sink
Obviously, Type 1 is most convenient.
Type 2 does have an advantage in energy savings. Often, with a single handle, a user will leave the handle somewhere in the middle, such that it draws water from both the hot and cold pipes. However, the hot-water draw is often unintentional. The user will just wash his/her hands for a few seconds, not long enough for the water to get warm, and not really caring that the water is cold. Nevertheless, drawing cooled water from the hot side does have a consequence, since the hot water tank will need refilling. Therefore, users of single-handle mixer taps will often unknowingly waste energy heating water for absolutely no benefit. (The Swiss government, for example, runs a campaign to remind people to keep the lever turned all the way to the right, which would not be necessary with a two-handle system.)
The British, though, seem to be stuck on Type 3. Part of the reason is a fear that a dirty heater tank could contaminate the cold water supply if mixing were allowed. Mostly, it seems to be a case of stubborn conservatism.