I arrived in the UK any my first batch of pets arrived after five days, followed a week later by my second batch. They travelled outside the five day rule. More paperwork was required and, of course, this meant a fee for completion. I found the following which seems to make it clear:
https://www.pettravel.com/immigration/England.cfmCommercial Transport: the owner or a legal representative of the owner is not traveling with or within 5 days of the pet OR the purpose of the transport involves a sale or transfer of ownership OR more than 5 dogs, cats or ferrets are traveling with or without their owner.
Commercial Transport to England from a rabies-free or rabies-controlled country outside the EU:
Regulations in steps 1 and 2 apply.
A licensed veterinarian in the originating country must complete the commercial EU health certificate within 48 hours of travel. If your pet is traveling from the United States, the veterinarian must be accredited by the USDA for endorsement by the State USDA unless the certificate is completed by a military Veterinary Corps Officer or GS-0701 series civilian government veterinarian employed by the military.
The CFIA must endorse forms issued by Canadian veterinarians.
If traveling to England from another country, then the forms must be endorsed by the government agency responsible for the import and export of animals.
This form is good for transports of 5 or less dogs, cats or ferrets. (see step 7 for transports of more than 5 pets.) The form is good for 4 months of travel within the EU as long as the rabies vaccination documented on it does not expire.
Your pet must enter england at an approved Border Inspection Post (BIP) at an international airport in Heathrow or Gatwick. Notice must be given a minimum of 48 hours prior to arrival.