For every sink / basin / bath / shower with a mixer tap:
1. Turn the hot on, and feel the hot pipe as close to the tap as possible.
2. Turn the cold on. If the hot pipe starts to feel cooler, then water is flowing back from the cold into the hot.
A mixer tap is one where the hot and cold are mixed internally, whether or not thermostatically controlled. A tap which feed cold through the outside of the spout, and hot through the inside (or vice versa) so that hot and cold only mix immediately after leaving the tap, is not a mixer tap for the purposes of the above test.
It is also possible that the bath / shower has a thermostatic mixing valve fitted. This is a valve, usually hidden from view (e.g. under bath), which blends cold water with the supplied hot to output hot water not exceeding a certain temperature (usually 38 or 40 degrees). They are in effect mixers as above. Often fitted in newly built or newly renovated properties, and those designed for the old and infirm.