OK, I could take issue with a few of the points in this rant by ianzin. But instead I’ll point out that this is the GQ Forum and ask in what way is any of this even remotely relevant to the OP???
Isn’t fully pressurized hot water a benefit in and of itself? In the US, the pressurized cold water is fed into an enclosed heating tank which feeds the hot water pipes. It’s pressurized the whole way, so your hot water has the same pressure as your cold water (well, it varies a little, since the heater can corrode and impede water flow). A water heater is only $200-300, and seems vastly superior to a system that’s gravity-fed from an open tank.
Perhaps if it was common for people in the US to wash their hands in a basinful of water and to take regular baths, we wouldn’t care about this issue either. But I don’t think I’ve ever seen anyone fill the basin to wash their hands, and taking baths is mostly reserved for 1) children and 2) women who just want to be left alone for an hour. 
And (I’ve been told) by (3) some people for treatment of hemorhoids (sorry 'bout the spelling).
If you didn’t have mixer taps, you’d probably see it a lot more and if people were used to filling a basin/bath, the perceived need for mixer taps would be diminished - sounds like circular logic and I suppose it is - the whole thing is a vicious circle; No mixer taps>different habits>no demand for mixer taps>no market for mixer taps>no mixer taps
Personally, I think that the reason for the persistence of separate taps in the UK is down to the habits of builders - at least until fairly recently. Usually, a new house will be fitted to a minimum standard and two separate taps are a little cheaper than a mixer - so that is what you will find originally fitted in a new-ish house.
As time goes by, people will refit bathrooms and kitches to their own taste and may or may not decide to fix mixers so there is a slow drift towards having mixers. I’d guess that people only totally refit a bathroom or kitchen every twenty years or so on average. Besides, AFAIK the really nice reliable ceramic valve tap types have not been available for more than a few decades.
Also to take into account is that British tastes are often quite conservative. Many people may opt for a smart but old fashioned look: edwardian bathroom, country cottage kitchen etc.