My experience was great, I'm very pleased to say. The vet tech who helped me all the way from the beginning was such a trooper. The day before the flight, some paperwork had to be reprinted and signed by a vet at the last minute, but she got it all done. In hindsight, doing this process on your own is not as bad as it seems when you're faced with it at first. Just allow yourself enough weeks (or months) to get it all done; check, re-check and then check all your paperwork again and don't be afraid to speak up if your vet is doing something incorrectly (not signing in blue ink, not dating paperwork dd-mm-yyyy, etc) as it will save you some hassle. Also, I emailed all my documents ahead of time (plus pictures of the carriers) to Virgin Cargo and HARC. They advised me of any changes that needed to be made and I would highly advise anyone else to do this as well.
On the Atlanta side, I had to spend about an hour and 10 minutes having all the paperwork processed at Virgin cargo. They measured the animals and carriers (so glad I went a size larger for the 2 dogs), made sure everything was signed and dated correctly, had me take all collars off the pets (but I could leave toys in the carrier) and once I paid, I kissed them goodbye. At the gate, I was called to the counter and they told me my pets were safely on board.
At LHR, my husband and in-laws picked me up in a van and we drove about 35 minutes to the Animal Reception Centre (it is not close to the arrivals terminal, so you must have transportation). You are told it can take 4 hours to get your pets, but after only 1 hr 45 minutes, they were released to me once we paid the fee. The dogs were on their leashes and looked happy. The workers had let them out for the bathroom and fed them the food I taped to the carriers. Kitty had fresh bedding (although it was shredded paper) and only looked slightly traumatised by the whole thing.
HARC asked if I wanted to leave the pet carriers, but since we had a big van, we packed them in and drove home to Wales.
Overall, it was a very pleasant experience. I felt that Virgin handled me and my animals with care from beginning to end.