I don't have a whole lot to offer, but, wow, plumbing culture in the UK sure is different from the US.

I assume "mixer shower" is one where it takes cold and hot water supplies and mixes them together to achieve the proper temperature. So, a standard shower in the US.

I had to look up "combi boiler". This appears to be a tankless water heater that also provides hot water for radiators (or other water-based house heating systems).

You use both of the terms "power shower" and "electric shower". It seems that an "electric shower" is a shower head that has a builtin heating unit. Do you mean "power shower" to be the same thing, or is it one that has a pressurizing system?

I don't see any reason that an electric shower would have any dependency on the water heater at all; it completely bypasses it. The only thing I can think of is that both of them would be large electricity consumers and maybe your service doesn't have the capacity to run them both at the same time.

I have a feeling you misspoke here: "we won't be able to use the mixer and the combi at the same time". Did you mean the mixer and the electric shower? If so, again, I don't see why not, other than power consumption. Have you asked your plumber why?

As to the thermostatic controls, if you're referring to the electric shower, if the pressure drops and you don't have a thermostatic control, that means that there would be less water flowing through the system, but the same amount of heat being generated, which would cause temperature fluctuations. I don't have experience with these systems, so I don't know how significant they would be. As for mixer showers, they have had passive pressure matching technology for decades now. Thermostatic controls are only useful if you specifically want to set a particular temperature, rather than fiddle with the mix.