@Gargron We generally use the cold to wash hands as it’s actually marginally warm. Or, the hot in the winter before the hot water runs through.
For the mixing you are supposed to use a plug and make a bowl and mix in the bowl.
This is literally Victorian technology and as a Brit 🇬🇧 I’m thoroughly pissed off this is still everywhere. The American way is far superior. Along with air conditioning.
I will however happily keep it in exchange for free healthcare at the point of use. So if you badly burn your hand just pop to ER and you will be seen at no cost.