Your cat or dog or ferret needs a microchip to identify them. And then once they are at least 3 months old, they need a rabies vaccination. Your vet needs to ensure they have read the microchip before the rabies vaccination and noted this on the vaccination card or clinical notes
The AHC (Animal Health Certificate) is issued by the vet within 10 days of travel. It is valid for exit FROM UK for 10 days after being issued. But valid for 4 months to return to UK.
Coming back to UK is pretty simple from Listed country or the EU (full list is here). Your dog will need a vet check and tapeworm treatment 1-5 days before they come back, your cat will just be able to come back.
Countries and Territories that use Animal Health Certificates