LuganoPirate, my understanding and having also been stopped and searched is that you have to be given, at the completion of the process, a form 5050 which explains why you have been stopped and your legal rights in the event of you feeling you have been unfairly treated.
If the person who stopped you is not showing any identity badges, you have the right to know from which Governement department they belong and the reason for the stop.
I agree about technology sometimes failing, but its all about your own system and making what works for you work. So if your system is to carry £3000 in cash for trips, I see no problem with that whatsoever, as long as you have some documentary or verbal reason as to why you have that amount of cash. The best paper support you can provide is a detailed itinerary along with a letter on company paper or from your bank confirming the source of the funds.
I can not see anyone at an airport being suspicious over that and I am sure you would be on your way within a couple of minutes.