Andrew, Check for 12v (+) on pin 6 and (-) on pin 7 of the car 12S socket when the car engine is running. {older vans (+) on pin 6 (-) on pin 3.
If the voltage is present connect it to the car with engine switched off . On post 98 vans switch on the caravan internal lights. Start the engine and the lights should go out - this proves the fridge supply is getting to the van ( the fridge supply switches a 'habitation' relay in the van which disconnects the supply on pin 4 (+) from powering the van 12v to charging the van battery.
If the lights go out check for 12v at the fridge. If it is getting there and the fridge is switched on then suspect the 12v element.