As far as I know animals, apart from guide dogs can only travel as 'freight' in a pressurized part of the hold. Heathrow has a special animal handling unit where all animals are sent on and collected off flights. You can not take an animal ,apart from a guide dog, on the plane with you, there are very severe penalties (including haveing the animal destroyed) for trying to get a pet on a flight. Coming back a dog MUST go into quarantine for 6 months unless it has had the full rabies tests and inoculations.
You can only take animals out of the country or bring them back in by using an airport that has a special animal handling unit and I think Heathrow has the only such unit in the UK.