Although the electricians are undoubtedly giving you all the right answers, I suggest you seriously think about a mixer shower. Firstly, you are allowed to do all the work yourself, without formal qualification, just common sense and some some practical ability. IMHO electric showers should only be fitted when a gravity mixer or power shower is virtually impossible to install. Your new shower is going downstairs, so you have the requisite head of pressure for the hot water supply and you will have to install a cold supply in any case.
IMHO, when installing a mixer shower you, or a plumber, will focus on pipework only. However, any new work on your electric supply, to enable installation of an electric shower will involve major changes to your fusebox, etc, which is far more expensive due to the legalities of notifiable work, which requires an electrician, who will have to inspect and repair your your existing wiring and distribution before actually doing the wiring to the shower. Given that you already have a shower, any delay in getting a plumber to do the pipework isn't going to be inconvenient.
You have probably already considered the option, but I thought I'd mention it just in case. Apart from anything else, in my experience, a mixer is a better (more powerful) shower anyway.
IMHO, when installing a mixer shower you, or a plumber, will focus on pipework only. However, any new work on your electric supply, to enable installation of an electric shower will involve major changes to your fusebox, etc, which is far more expensive due to the legalities of notifiable work, which requires an electrician, who will have to inspect and repair your your existing wiring and distribution before actually doing the wiring to the shower. Given that you already have a shower, any delay in getting a plumber to do the pipework isn't going to be inconvenient.
You have probably already considered the option, but I thought I'd mention it just in case. Apart from anything else, in my experience, a mixer is a better (more powerful) shower anyway.