Mike Cross has indirectly given you the right answer, which is, discuss your wishes with someone from an approved skydiving operation (the guys at your regular DZ should do) to see if they would be agreeable in principle. Then call the CAA, tell them what you want to do and ask them how you go about obtaining the necessary permission.
Plan B: Go to another jurisdiction which is not so picky about these things and try it there. From what you say, the States might be an option. Saudi Arabia is also a distinct possibility--I was invited to join a bunch of guys who would every now and then "get hold" of an Herc (don't ask
) and go jumping out the back.
As a skydiver and a pilot I don't think it's a bad idea per se, with the provisos given by Scooby, but you've got to go about it the right way.