Sorry - obviously didn't make it clear - the mains pressure is more
than adequate, hence the electric shower; it's the hot water supply
that has only a 3 to 4m gravity feed and this fancy mixer tap
recommends 0.5 bar minimum in the SMALL PRINT :(.

Yes, stick a single impellor pump on the hot side only. Use a pressure
balancing brass bodied thermostatic shower mixer valve. Run the bath hot tap
off it too.

Christian.