I had a similar issue in our place, 1 mains (combi boiler) fed shower and one electric. However, the cold into the house is only 15mm. So, barely good enough to run the mains shower alone.
My solution was to fit a loft tank and one of these (or very similar):
Salamander pumpWorks a treat and powers up the electric shower with good pressure. I then half closed the isolating valve that fills the tank, so it only drip feeds as the tank empties. Result: you can now run both showers at once with decent pressure
. Fitting the same on your tank outflow should cure your issues.
In terms of connections, this is 2x22mm push fittings and can be wired off to a three pin plug. You will need a negative rather than positive head pump as (most likely) the pressure/flow from your tank won't be enough to trigger a +ve head pump. In my case it would only trigger if I turned on both the shower and another tap - useless.
So far my salamander pump has been working just fine for about 9 months, you can hear it when its on, but I wouldn't say its noisy.
Hope this is helpful.