The only electrical fault that could occur on a fridge freezer, without simply blowing a fuse, causing a circuit breaker to trip out or setting the whole thing on fire, would be if the thermostat got stuck and the refrigeration unit was permanently running (instead of turning itself on and off every so often). Then a typical fridge freezer (rated at 250W) would use 6kWh per day, instead of perhaps 1kWh if it was running normally. So (based upon 14p per kWh) that would add 70p per day to a household electricity bill, or about £90 per quarter. Anything much more than that simply can't be associated with a fault in your fridge freezer.
Even so, it's unlikely that you'd ever get through a full quarter without noticing the fault, as the entire unit would probably be totally iced up within a week. So I reckon whoever told you that the cause of your high electricity bill must be a dodgy fridge freezer probably doesn't know what they're talking about!
Either way, it's your responsibility to ensure that any electrical appliances in your home aren't using excessive electricity, so they'll expect you to pay up. (However electricity suppliers are usually sympathetic to customers who experience problems in paying their bills, so they should let you spread the additional cost over the next few quarters if you contact them).