When I moved to London 4 years ago, I called each airline and asked about their pet transport service. Most were willing to send me email FAQs. I chose Virgin (even though I have over 800,00 miles flown with AA and was a Platinum AAdvantage card holder) because I could make a firm reservation for my dog, and they don'take the pet to the airplane until they were ready to load them on the plane. Some airlines (AA) take them out to the tarmac and let them sit while they get the rest of the cargo on board. The noise and commotion would be very stressful if an animal has to sit there for a long period of time. Because AA loaded pets this way, they couldn't guarantee the pet would go on the reserved day. If the weather is too hot or cold, they can't leave the pet just sitting on the tarmac. Not leaving as scheduled can be a real concern, as animals arriving under the pet passport scheme have to have shots in a very limited time frame before departure and must be crated/sealed up by the USDA. If the pet doesn't go on the scheduled day, that could really mess things up. Also, AA was not willing to change my flight (without a huge charge) to go on the same day as my dog if there was a weather delay. So there was no question in my mind that Virgin was the way to go.
I don't know who flys from SEA to LGW, but I think it would be best if you call those airlines directly and find out their pet transport policies, and make your decision based on which airline can take your pet in the most comfortable and stress-free environment.
Also, you might want to consider flying them to Heathrow if that means a direct flight. It would be a lot easier for your kitties not to have to deal with the delay of a connection and the stress of being re-loaded on a second plane.
