Star whale

A Star Whale is a giant beast that swims around in space. There is now only one of its kind left, very much like the Time Lords.

Physical Appearance
The Star Whales were giant alien creatures, resembling Earth's whales in basic structure. They had several flippers and tentacle like protrusions on their backs. They were capable of surviving in the vacuum of space. (DW: The Beast Below)

History
"Imagine if you were very old, and very kind, and the very last of your kind; with no hope of a future, what couldn't you do - you couldn't stand and watch children cry."

An ancient and benevolent species, the Star Whales had, according to legend, guided early space travellers through dangers on their journeys through space. By the time of the 29th century, the species was all but extinct save for one, who is theorised to be the last of its kind. When Earth was facing destruction because of solar flares, that Star Whale was drawn to Earth. All the peoples of Earth had managed to escape in massive city ships, but the people of the United Kingdom lacked the supplies to create an engine. The people were left hopeless and mostly heartbroken by the sounds of their children crying due to the increasing temperatures. It was these sounds that had drawn the whale to the planet, for as Amy put it, “When you're that old and alone and so full of kindness, what else can you do?” The whale intended to offer its services to the stranded people.

Unfortunately, the people of the UK misinterpreted this gesture of good will as a chance in a million miracle. They captured the whale, building their ship right on its back and carving an opening to its brain to torture it into moving. The city built on its back became known as Starship UK. This led to the paradoxical situation in the ensuing years as the people began to realise they could not justify their survival off of the suffering of an innocent creature. But they believed if they released it, the creature would destroy the ship in its escape; so they devised the "Forget" system to erase their memories and the Smilers and Winders to ensure that no one discovered the truth and to “dispose” of those who didn't agree to have their memory erased by feeding them to the whale.

Eventually the Doctor discovered the heart of the ship, where the Smilers and their controllers were torturing the Whale with electric shocks to keep it moving, and faced the impossible situation. Angered that he would now have to sacrifice the life of an innocent and one of a kind being to save billions, the Doctor was prepared to lobotomise the Space Whale so it would no longer feel pain from the torture. Amy, however, noticed the Whale's neural tendrils affectionately playing with the children who the whale always refused to eat when they were sent down below. Remembering the Doctor's lesson about always observing she quickly put the pieces together and ran over to the control system to press the "Abdicate" button, freeing the Whale. The ship, however, did not explode as was originally feared but instead started to move faster "Well, now that the pilot's not being tortured" Amy explained, having deduced that the Whale had come willingly and was still willing to help the people of the UK.

The TARDIS then left, now that the people of Starship UK had a better understanding and respect for their benevolent benefactor. What was unnoticed however was another crack in the universe that ran across the side of the space ship. (DW: The Beast Below)

Behind the Scenes
The idea of the Star whale carrying a society on its back is a possible homage to Terry Pratchet's Great A'Tuin the Giant star Turtle who carries the Disc on its back. It also may be a re-write of the abandoned Pat Mills story Song of the Space Whale

The motif of a starship built on a sentient being appears in another realm of sci fi, Marvel Comics' X-Men. The Acanti, a similarly benevolent race of space-dwelling creatures resembling whales, were enslaved and used as interstellar transport.

The motif also appears in the AD&D Spelljammer campaign setting, in which The Spelljammer is a legendary ship which looks like a gigantic manta ray, and houses an entire city on its back.