Shower pressure varies between hot and cold

Sconsey

Hi,
I have a shower that is fed from the hot water tank, there is a pump that kicks in whenever I turn on the shower. There is a significant difference in water pressure when I have the shower running cold water compared to when I have it using hot water. I initially thought limescale in the shower head might be a problem so I got a new shower head, very little difference. My next thought is possibly a limescale buildup in the hot water side of the shower mixer? is this something worth investigating? it would mean me having to remove the mixer so want to know if I am wasting my time before attempting that job.
Another question, which I should really know myself, does both the hot and cold water go through a shower pump or is the cold water usually fed directly from the water tank in the attic? I am assuming they are both pumped for the shower.
Thanks

Sleeper12

Bot the hot & cold "should" go through the pump and you "should" have equal pressure going into the shower.

Assuming you have the above then the hot filter could need cleaning or the thermostatic cartridge might need to be replaced