All documents (each one MUST be an original except for the rabies test results which is a copy but with an applied label showng the results) are handed in to the airport staff dealing with checking live animals.
The staff okay everything then put all papers into a plastic bag which is then attached to the top of the kennel/crate, and flies with the animal; you don't see the documents again until pickup in the UK.
At the animal recepetion center at the UK destination, the staff there will then go over those documents and make an examination of the pet before okaying him or her to be picked up by the owner.
Basically every document you prepare is out of your hands once you check your animal in, and the staff take care of the rest.