While either a Part P-certified plumber or electrician can install an electrical shower, you are better off working with a Part P-certified electrician. This is because the competence and specialty of a plumber will likely be more focused on just the plumbing aspects of the installation and won’t cover the electrical aspects.
Electric showers combine water and electricity, which means it is crucial that their installation or repair be performed safely and correctly. If you are installing an electric shower from scratch, a Part P-certified electrician can install (or upgrade wiring) and check wiring to ensure everything is working safely. However, if you are simply replacing an existing electric shower with a similar one, a plumber will be sufficient as the needed electrical cabling will already be in place.