I'm slightly confused. I, too, have a combi boiler as well as a Mira electric power shower. The only reason I have the combi boiler is because there was nowhere (high enough above the bathroom) for any water tanks. But if you do have a tank, I don't think you have to have a combi boiler rather than a traditional one.
Anyway, I just wanted to say that I have had similar problems to yours in the past. In my case, opening the stopcock to just the right amount is fairly critical because, on the one hand, the incoming water pressure for the boiler mustn't be more than a certain amount, and on the other, the cold water pressure to the Mira must be more than another certain amount, otherwise these units don't function correctly. And in the case of the shower, I think that it will shut off the water flow if the pressure is too low.
Your Mira unit should be supplied with cold water from the
main, and not indirectly from any tank. Your bath, etc, should be supplied from the tank, and it sounds as though your boiler is, too.
So, to get to the point (at last!), I suggest you see if you can open the stopcock a little further. If you have definitely done that already, then the other thing I would suggest, assuming you live in a hard water area, would be to descale the shower head.
Good luck.