We have a new shower rose installed. When starting a shower we have to turn it onto full hot (we have a mixer), then move it slightly towards cold to get it about right. 1mm left or right it is too hot or cold. Because it is at the hot end, the water pressure is not great. Our water tank is in the ceiling and the shower is 2 floors down.
It sounds very much like your cold water pressure is significantly higher than your hot water pressure, and the mixer valve can't cope.
Presumably this is because the cold is at mains pressure (probably 2-4bar, or even greater), but the hot, coming from the header tank is at about 0.6bar (assuming 20ft height differential from tank to shower).
Most mixers require hot & cold to be at the same pressure. You need to either achieve this by running a cold-feed from the same header tank, or replace the mixer with a suitable type.