PETS Scheme
Islander2 beat me to it but here is the actual words from the DEFRA website.
PETS: Dogs, cats and ferrets
Routes and transport companies;
You may use any of the routes and transport companies on the following lists to bring your dog, cat or ferret into the UK under the Scheme, subject to the transport company’s agreement. All companies have been approved by Defra to carry dogs, cats and ferrets but not all may wish to carry ferrets. There may also be a limit to the total number of animals that a company will permit to travel on each boat or aircraft. Check with the company before booking your tickets that they are prepared to carry your pet.
You may not bring a pet into the UK from a private boat or plane.
I too would like to take our dog in the aeroplane but there you go.