Not for anything other than completely stripping your paint back prior to a full detail. You see, Fairy Liquid is not as highly concentrated as car shampoo and it’s designed to cut through things like grease, which isn’t necessary on your car.
It’s also designed to clean products such as china plates and stainless steel cutlery, products that are easily able to handle this abrasive cleaning agent. Your cars paint is much more fragile, so if you do decide to use it, approach with caution.