I'm usually reluctant to recommend pumps as they SEEM like a waste of electricity. But I worked out a comparison once for a customer and the extra wasted heat from the water content in the 'dead leg' of the the 22mm pipe runs compared with 15mm pipe runs and energy used by a pump showed that pumping the water through a smaller pipe saved energy (and that was for a full-size shower pump, not an inline Shower Power Booster which, while not being quite as powerful, uses much less energy and is cheaper to install) If installed correctly, pumps should last quite a few years, though that no longer seems to mean 20-30 as it used to in the old days. The warranty may length may give you some idea of durability, though I have known cheap pumps last for 10 years or more and you may be lucky.
The OP's plumbing looks like an old system that has evolved over the years. These types of systems often have pipe runs that reduce the available head of pressure at the tap along their length due to numerous joints and poor plumbing practice by at least one of the many installers (the plastic pipe will have smaller bore than copper and that doesn't help either!). Or, as has been suggested, partially shut or small-bore valves. The standing head (height of water level in loft cistern above the bath taps (1bar =10m.)) is probably less important than the pipe runs.
In my own house, I have improved the water flow from my existing bath tap from 4 litres/minute to 22 litres/minute just by putting a new 22mm pipe run between the cylinder and the bath. But then I was meticulous about deburring, minimising pipe length, and getting my bends as smooth and streamlined as possible and wasn't concerned about energy use as the bath is not used often and mostly in winter.
The OP's taps (if that link is correct) show a flow rate of 4 litres a minute at 0.1 bar. This will be at the working pressure (i.e. standing head as above MINUS any loss of head along the pipe run). It is quite possible that the available head (working pressure) at the tap is only 0.1 bar on a gravity system. If the OP's taps are running much faster when running cold, the installation may have mains cold and cylinder hot - it's more common than people think.