Loosehead is wrong.
Economy 7 is just cheaper electricity overnight - however it is used. If you have an immersion heater it will be cheaper to heat the water overnight.
Similarly with storage heaters, tumble driers, washing machines.....
However, your electric shower will heat the water as you shower. The higher the flow, the cooler the water. At this time of year the ambient water temperature is cooler anyway - so the shower has to work harder to heat it.
Try turning the shower DOWN - so you get a less powerful flow.