Pumps
Hi Pete,
If the only 'real' problem is the shower, then I can suggest two solutions.
1) Install a pumped instant electric shower. This heats the water and boosts the pressure. The one I have is a Triton, I think a T90si, and it's the business.
2) You can also install a pump on the hot water feed to the ordinary shower. I have this done in my bathroom, and it works really well too, in fact it generates more pressure than the Triton, but it doesn't do anything about heating the water obviously. If the shower is above the bath, then they can put the pump under the bath.
I can't recommend anyone to do these, as I had them done when the house was being built, but any plumber should be able to do this, and they usually know an electrician who can do the wiring.
Philly