I was in the exact same predicament 6 months ago. I went to my local refuse centre, I was told when I got there "You will need to apply for a permit, which should arrive within five days" all this because I was in a car derived van. It was a 14 inch portable TV I was wanting to dump for Christ sake, not a skip full of rubbish.
The thing was, I had just borrowed the van and then was the only time that I could have disposed of it.
All I can say is, with bureaucracy like that, then no wonder there is fly tippers.