Most straightforward way to measure pressure generated by gravity (your present hot-water system) is, every metre above the draw-of point (shower head on the riser rail - most likely) generates 0.1bar. i.e 10m difference in height = 1.0 bar.
So, likely maximum pressure (static - when water is still) would be 0.2-0.3 bar in a bungalow.
AND, DO NOT mix mains pressure coldwater and tankfed hot-water in a bath/shower mixer. the cold water will push any hot flow back towards the storage vessel. Even (double)check/one-way valves (as required by water regs) would be problematic as it would further restrict hot flow through them to the bath/shower mixer.
So, I would suggest either, a) (cheapest) tank fed cold water - at same pressure as hot, & a shower pump to boost filling/flowrates - you may need to enlarge both capacities of hot-water storage vessel/domestic storage cistern in roofspace to minimise water starvation.
b) dearer, a mains pressure unvented cylinder with balanced hot&cold pressures
c) possibly dearer yet, a 'combination' boiler oil/gas to provide effectivley mains pressure instantanious hot water provision.
d) (not very likely) bury the bath so deep in the floor you get 0.5bar pressure.
DH
BTW, if you are in an NR postcode I am happy to provide a competitive quote for a) to c)