Can you fit an pump to a gravity fed electric shower

The pressure in my area is low, I have purchased an electric shower which is mains water supplied, unfortunatley if any other tap is turned on the shower turns of the heater and the shower goes cold.
If I put a tank of sufficient size up in the loft could I then fit a pump to a single cold water gravity feed to give the required minimum pressure 1 to 3 bar (15 to 45PSI Approx).

This is a fine solution to a common problem.

Your alternative to a separate pump (having installed the new cistern) is to replace the shower with one that incorporates a pump, but the cost would be similar to that for a separate pump.

The Inspector said:

The pressure in my area is low.

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The problem is not the pressure but the flow rate. You may be able to improve the flow rate, for example by making sure stop taps are fully open.