In the UK, hot and cold water is still delivered to the taps in separate pipes
I think you'll find hot and cold water is delivered in separate pipes all over the world. ;)
But I know what you meant. There's actually a very good (semi-historical) reason for that.
In most UK houses (older houses certainly, I'm not sure how it's done now) the hot water heater is fed from a cold water storage tank in the roof, which in turn is fed from the mains pipe opened and closed through a ballcock similar to the average toilet. (I.e., the surface of the water when the tank is full is below the pipe feeding it.) The tank in the roof also feeds all other cold water taps in the house except for the kitchen sink which is supplied straight from the mains (and is the only cold water tap you can safely drink from).
This arrangement means that the water pressure, at least in the kitchen, is usually different between hot and cold taps, so installing a mixer tap could potentially allow cold water to push back into the water heater if the mains pressure was sufficiently high, ultimately flooding the house from the roof down - although that's probably quite rare given that the tank in the roof will have an overflow pipe leading outside the house. It's usually safe to installer mixers in all other rooms - unless they too are fed directly from the mains.
Setting up the pipes like this ensures every household has a small, clean supply of both hot and cold water in case of a burst water main, and also that if the mains pressure does drop opening a tap doesn't allow contaminated water (from whatever source of contamination) to feed back into the mains (thus spreading the contamination further).