Unless you are willing to upgrade the hot water system in the flat then it is unlikely you will be able to install a mixer shower.
It would make sense in this case to install a good quality electric shower.
You say your "concern is that it would not work well due to low/erratic mains". The electricity board is obliged to give you an uninterrupted supply, and for safety's sake if nothing else, your internal wiring should be to current standards. Poor supplies may damage other equipment such as computers and televisions. So I would give consideration to curing this fault as part of your flat renovation.
DIY how to tutorial projects and guides - Did you know we have a DIY Projects section? Well, if no, then we certainly do! Within this area of our site have literally hundreds of how-to guides and tutorials that cover a huge range of home improvement tasks. Each page also comes with pictures and a video to make completing those jobs even easier!