ok lets get the basics out of the way..
do you have an immersion heater?
is it on a timer?
is it perhaps wired into the socket circuit?
do you have under floor/tile heating in the bathroom etc?
you mention oil.. does the tank have trace heating to keep the oil at a useable temperature?
1) Yes, but it is switched off and hasn't been used for a few years, so not on a timer. I'm not 100% certain which circuit its on and can't check due to time now, will edit in the morning.
2) No underfloor heating anywhere in our bungalow, a radiator (or two) in each room bar the kitchen.
3) No, just a plain garden oil tank no trace heating or gadgets.