Difficult to tell without seeing it.
There are regulations in Scotland governing what you’re allowed to do electrically. I’m Wales based and our regulations are different to yours but I guess they’ll require some level of notification or professional input.
Your night storage heaters will almost certainly be on an off-peak rate which is not fed from the modern box. If you’ve got three big fuses I would guess there are three night storage heaters in the house? Or, two plus the immersion heater.
You’ll need to connect into one of the off-peak circuits (which should be dead off-peak, the peak depending on the tariff you’re on). It is normal for one fuse per heater. Assuming they’re 3kW thats 13 amps per heater and the fuses/cabling are probably only rated at 15amps (guessing rewireable fuses)so you’ll need to reroute the existing cabling for the heater you’re moving to it’s new location as it would blow the fuse if more than one heater was put on each circuit.
Because of the possible complexity of the installation you’ve got I’d respectfully suggest that this one might require some professional input on site just to make sure.
Rich.