The definitive answer...I hope:
Washing-up liquid (Fairy Liquid being one of many brands) is a powerful cleaner and degreaser, but the problem with it is that it contains Sodium Chloride (salt) which is used to add to the viscosity. It may also contain ammonia.
Salt makes water a better conductor of electricity and because the process of oxidization is essentially an electrical process, the addition of salt to your car’s bodywork speeds up this process.
Oxidization is bad for both your paintwork and metalwork.
Washing-up liquid can also contain other chemicals such as solvents, surfactants, colourings and preservatives which may be fine for your dishes and hands, but may not be so good for your car.
Some things just belong in the Kitchen
Washing-up liquid is especially formulated for washing grease and food from crockery, so when washing your car it is best to use a soap especially formulated to remove salts, tar, pollutants and traffic film without causing damage.
Fairy Liquid is no exception and will strip all the wax from your car, it may also make your paintwork dry and brittle and prone to chipping and even cracking.
I used to use it to aid in the removal of waxes before I knew better....I don't anymore!!
You should use a purpose made car shampoo that contains no salt or salts. These can be purchases quite cheaply from motor accessory shops, either in sachets or by the litre. ...so why would you use washing up liquid??
Hope this helps you in your decision in the future when filling the wash bucket
Chris