Sounds very dodgy to me, dont know how they've managed to balls it up. As the others have said though, always ring up and make sure they take payment properly. The only near experience I've had with Admiral they were actually ok. My CC had expired and they called me up to check the number for the auto renewal. I told them I didnt want to renew as a new quote was cheaper so they matched it there and then.
I guess working in IT I can understand when systems have blips and things can go wrong, so I never assume that auto anything will work