No hot water through downstairs mixer tap! Please , any ideas.

Just my initial idea based upon the information that you have given would be, if there is a shut-off valve under the sink for the hot water, then I would try tapping on it with something like a hammer. Turn the valve to try to loosen anything that might be stuck in there. Sometimes debris can get built up in those valves. I have tried this method and had success with it.

Maybe someone else on this site will have a better idea, though.

Sounds like you have mineral buildup in your water heater and now its got sucked into your faucet. Shut the water off to the faucet in question and open it up. Check and clean the inlet ports on the cartridge or seat and turn the water back on for a moment to flush out any crud remaining in the supplies. To prevent this from happening again flush your water heater. Let me show you how.
For long life and fewer troubles you should keep your heater clear of mineral build-up by flushing on a regular schedule. Attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run until the water runs clear. You will see a spurt of red,(rust) followed by white or yellow grains,(lime or calcium carbonate). This shouldn't take more then a few minutes. Do this monthly to keep it clear. Now flush out your hot water lines on ALL fixtures that are affected . Now pull each aerator and clean the screens. Be sure you put them back togather the same way you took them out. Don't forget to flush it out every month. Your heater will thank you for it. Hope this helps, Tom