It might if the plug is moulded onto the lead, but I doubt a fridge/freezer needs a 13A fuse. That represents a maximum power of about 3kW!
See if the appliance's instruction-book advises on the correct rating.
Have you tested the fuse itself? They can blow by age even if the equipment is fine, though I don't think that is very likely unless it takes brief maximum currents frequently, as it might each time the motor starts. If it had been running for a long time with a 3A fuse, replace it with the same or 5A.
Though I have just looked at the photo again. That is a 13A fuse so had you replaced it?
