OK many thanks for detailed advice. Makes sense.My family plumbers recommend you stick with a roof tank and water pump. I have checked what flows and pressures your shower requires and these are easily met by the tank and pump and in range for minimum and maximum pressure and flow rate. If you dispense with the pump then you risk changes in pressure and flow rate when other taps and water using appliances are drawing water which the shower's stabiliser may not be able to compensate for. If you do without the tank and the pump then with regards to pressure and flow rate you are at the mercy of the local water company and its distribution network plus the consequences of neighbours drawing water at the same time causing lower pressure and thus lower flow rate. The tank and its pump provides you with an accumulator (reservoir) to ride through these variations in street water pressure.
Your pump can provide a flow of 3.2m3 an hour or 50L/min. The shower requires 8L/min or more.
The minimum pressure for the shower is 100kPa. The pump provides 12m head of water pressure which is about 115kPa and this is less than the maximum allowable shower inlet pressure of 1000kPa.
What they did suggest is that you fit a second pump in parallel with the current one but isolated at inlet and outlet using valves. Then if the main pump fails you can quickly bring into service the standby pump. Might be useful since you have a wife and children. You will need isolating valves on the main pump too at inlet and outlet. You get the idea.
Next challenge is to get the cold water feed from the current mixer tap in the shower to the electric shower without breaking walls and tiles.