I flew my dogs from Germany into Heathrow on Lufthansa (long story), and I think the Animal Reception Center is run by James Cargo Ltd. Their fee is for collection and transport of the animals to the ARC and the exam the animal goes through to be certified for entry into the UK. Their fee was included in the quote I got from Lufthansa, but not every airline may do that. The James Cargo people are absolutely wonderful -I was in touch with them (as well as Lufthansa) in the course of planning the dogs' travel, and they answered every question I had and were extremely reassuring. The dogs were picked up in an a/c van and the ARC people let me know when they had arrived. It took about 30 minutes for them to be cleared.
Here are a few tips about the ARC: Absolutely make sure you have directions on how to get to the ARC before you go. It's sort of in the underbelly of the Heathrow service areas, and my cab driver had no idea how to get there (he also didn't speak any English) and neither did the airport staff (the ARC building does have a weird 70s architecture tower with a large Q on it, for visual orientation). I had to take a 'mini-cab' because apparently black cabs won't take a short-distance fare like that. That being said, the ARC staff were able to get me another cab fairly quickly after I'd collected the dogs, and it wasn't a problem having the dogs in the cab.
The waiting room of the ARC is in a glass addition to the building, and it is absolutely boiling in there on a sunny day. If you can, bring some water or something else to drink/eat while you wait for your animal (they have a soda machine but it didn't work when I was there). There are some magazines to read, and fairly comfy couches. There's also a restroom, and a small grassy area to let your dogs relieve themselves and walk a bit.
You go in and ring a bell at the door and tell them what animal you're there to pick up, and they will bring the animal out to you when it's been cleared (they also provide updates, as I said). When I was picking up Ede and Atze, there was a couple waiting with me who'd come in from Canada, but their dog hadn't received an approved tick treatment and so the dog had to stay for another 24 hours (my dogs had gotten Frontline, and I just assumed that everybody would just use that).
Hope this helps!
Ness