This depends on what the airline requirements are for flying your cat. Your cat will need to visit the vet up to 2 times, plus you'll need to mail/fax/bring in your EC 998 form to get signed off by the USDA vet (no need for your cat to go anywhere, though).
Visit 1: microchip and/or vaccinate for rabies, and fill out the EC 998 form
...wait 21+ days...
USDA: sign off on the EC 998, which allows your cat to travel in the next 4 months
Visit 2: get any forms signed off for the airline (health certificate, APHIS 7001, etc). Generally these are valid for up to 10 days before travel, so you won't be able to combine this with visit 1, unfortunately.
DEFRA only requires step 1 and 2, but airlines usually require some sort of "yes, this pet is healthy" sign-off from a vet close to travel time (I've had to do this before a domestic and international flight for 2 separate cats).