Most fridge/freezer appliances (in the US at least) are actually one appliance with a single mains plug and control panel. They achieve different temperatures in the two compartments by wasting colder air from one side to the other with an adjustable damper. (Some models do employ separate coolant loops, but they are less common.)
Your Hotpoint (UK) model, if it does indeed have two mains plugs, might instead simply be two individual appliances that are packaged as one for convenience. In that case, you should be able to run just the freezer and leave the refrigerator unplugged and unused.
The likelihood of this working increases if the fridge part and the freezer part each have their own control panel. If there is a single shared control panel, running only one half may not be possible.
Try plugging in just the freezer plug. If the freezer works and the fridge remains dark, then I think you're OK.