You can get taps that do mix the water before it comes out. They are called single flow taps as opposed to dual flow taps.
Hi Mary, and welcome to the forum.
One thing you need to watch with using a single-flow mixer is the comparative hot & cold water pressures though. With the traditional (British) vented hot-water system, the hot at the kitchen sink is at much lower pressure than the cold, and a single-flow unit will result it being quite tricky to adjust the flows for the right temperature.
With the pressurized systems which have gradually been becoming more common for new homes and rebuilds in recent years, the hot is delivered to the sink at the same pressure as the cold, and the true mixer tap then works fine (which is how it is in the U.S.).
It's quite common to find the traditional dual-flow unit fitted to kitchen sinks even where a single-flow would work, as they are so widely available and have for years been the norm.