If you're moving pets to the UK, you'll need to comply with the Pet Travel Scheme (or PETS).
However, what happens if you are only having a layover with pets in the UK? Do pets need blood tests or to be quarantined? Where will your pet stay during the layover? This is normally known as a "transit" or "transhipment" and the rules are a little different.
DEFRA, the organization that oversees all of the UK pet import/export legislation, asks that people transiting with pets in the UK in under 48 hours to follow these rules:
If an animal comes into and leaves the UK within 48 hours from the same port or airport this is called a transhipment. If you need to tranship your pet in the UK, you must arrange this before your pet leaves the country of origin. You must ensure that, while your pet is in the UK, arrangements are in place to hold and transfer it from one plane/vessel to another for export. The travel agent/airline/ferry company should be able to arrange this or, if your pet needs to remain in the UK for between 4 and 48 hours, provide you with the contact details of temporary holding facilities at the port of transit. No licence is required if such arrangements can be made.
If your layover will be longer than 48 hours or if the airport you are transiting through doesn't have the ability to hold animals, you will need to do the following:
Where temporary holding facilities are not available, or if your pet is going to be in the UK for longer than 48 hours, it must be licensed into an authorised quarantine premises and may not be kept at the airport/port. You must contact an authorised quarantine premises, who will arrange for an import licence to be issued by Animal Health (formerly State Veterinary Service). This must be done before your pet travels to the UK. Animal Health will not issue the licence until they have received confirmation from your chosen quarantine premises that a place has been reserved for your pet. Most of the quarantine premises also act as carrying agents. Only an authorised carrying agent may transport your pet from the airport/port to the quarantine premises and back again.
For more information on moving with pets in the UK, check out the DEFRA website.