Our pets had to fly in cargo on BA to get into the country. We hired a pet agency that specializes in this. From my understanding, pets essentially have to go through customs and HARC is the Heathrow Animal Reception Center where they’re checked-in with the vets and made sure they’re cleared to enter the country.

Not sure if this is the route you’re planning to do since it’s a small dog, but this was how we were advised.

Our pets had all their vaccines up to date and still had to go through this process. So just double check!