I've seen 80's installations a plenty where the electrician has installed a point for connection of an immersion, but one was never fitted. Perhaps it fell down the gap in supply between the plumber and the electrician.
Two typical installation methods are shown below (earth omitted for clarity)
Try and determine which you have. If the isolator in the airing cupboard doesn't have a red indicator light on it, generally, I would expect there to be another operating switch elsewhere. Not always easy to find though. I discovered one behind a fitted kitchen in the past, and the householder didn't even know it was there. If you do have one hidden somewhere, the problem may be that it's switched off. If so there won't be any power to the airing cupboard isolator.
If you don't have the extra switch, then just swap the isolator in the airing cupboard for a fused connection unit, and connect the shower pump to that.
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