I have a very nice mixer tap in the bathroom which works fine with cold water but gives very little hot water. I don't want to throw it out as it is very expensive.
Virtually any tap can be repaired, but whether it is worth it or not is a very different question. If it is the older, "turn the handle many times" to open / close, then its usually straightforward. The more modern 1/4 turn taps are more problematic. They have "cartridges" inside with two overlapping ceramic discs to provide the seal. They are nearly all different, particularly with regard to how the handle is secured, and unless you know the make and model of taps it is usually very time consuming (for which read expensive) to find replacements. Thermostatic mixer taps will also have a thermostatic cartridge - usually eye-wateringly expensive.
You state that yours are mixer taps. These often have filters and non-return valves built into them, usually where they connect to the incoming pipes. These can become blocked with debris / lime scale resulting in poor flow. Removing the taps and dunking in something like Killrock will often free them up without changing any parts. However, unless you do it yourself you will be paying London rate for someone to do it for you.
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