Firstly, Washing up liquid is really not a good idea. It contains far too many ingredients that can be quite damaging for a car. First up the be damaged will probably be all your rubber seals and plastic. It can dry out these.
What i normally tend to do is snowfoam the car with an all purpose cleaner. Let that dwell, then rinse it off.
Then i would clay the car, then I give it a Wipedown with IPA.
You might think this is a bit overkill, and in some scenarios it is, but there are some pretty strong sealants out there.
Some might come off with an APC, but stuff like collinite can be a pain to remove.
Zymol vintage and royale sometimes give me a headache, but with those three steps above, your pretty much sure you have removed it all ;)