We picked up our dog and two cats at Heathrow. My partner had been on the same flight, although I doubt that made any difference. The paperwork was a nightmare, but picking them up was fine. About the paperwork, though: DEFRA only told us about part of the paperwork. It wasn't until my partner went to the USDA vet for the final wave of the magic feather over the stack of paperwork our vet had put together that she found out it wasn't complete. So listen to the USDA vet, not DEFRA.
By the way, we were afraid the trip over would be hard on the animals, but it was fine, and so were they.