If you have two taps, then the hot water and the cold water are completely isolated from each other until they mix in the basin.
Kitchen mixers are designed so that the two flows cannot mix until they emerge from the spout. If you look carefully you can often see a separate pipe inside the spout. However some modern "joystick" mixers with ceramic valves can wear and, when faulty, allow the waters to mix inside the pipes. This can lead to some tiresome problems. Some flashy stylish continental designs give poor flow at British pressures, and UK taps are often larger.
Historically, UK cold taps at the kitchen sink have always been supplied with uncontaminated drinking water direct from the incoming water main, and hot water via a storage tank. Depending on local practice for historical reasons, cold taps in bathrooms might be mains or tank fed.
Now that hot water from combi boilers or from pressurised cylinders such as Megaflows are becoming more common, many homes no longer have cold water storage tanks.
Most other countries in the world brought in widespread mains water supplies two hundred years or so later than Britain, so they set up standards which were more modern at the time. Britain still has lower pressure water mains than many countries. The last Roman pipes in London were replaced within living memory, but most towns still have a thousands of miles of iron pipes that were laid over 100 years ago. These old pipes would be liable to leak or burst at higher pressures, and nobody has ever wanted to take on the expense and time needed to dig them all up and replace with new.
Dean Swift (author of Gulliver's Travels), who died in 1745, wrote to his water company in London complaining about poor water pressure in his upstairs taps.