You are never really going to get great pressure from an electric shower. Their great advantage is providing an instant hot shower at the touch of a switch, with no excess water heating.
A pumped shower requires an external source of hot water, eg, your immersion tank. It is also a different set up in that you will need both a hot and cold supply plumbed to your shower unit.
There are basically two different pump shower set ups. You can get a shower unit with a pump located in the box (that goes on your shower wall) - Triton, Aqualisa and Mira do these - and probably others. Or you can locate a mixer on the shower wall with a seperate pump, eg, in your hot press.
The simpler job is to replace your electric shower, but you are not going to get power shower pressure. If going this way the new Triton silent (forget the name) has a good reputation.