Sentient oil

A puddle of sentinent oil was left behind on Earth, Bristol. The oil was able to mimick other beings. (TV: The Pilot)

Heather has previously come across the puddle, noticing something strange in her reflection. She took Bill with her to show her the puddle, who also noticed something strange in her reflection, however didn't learn much before Heather had disappeared.

Bill later returned to the puddle and found Heather looking into it again. Heather promised she wouldn't leave again but by the time Bill arrived to the puddle she was gone again, however Heather was inside the puddle unknown to Bill at the time.

Bill told the Doctor about the puddle, who before she finished explaining had already run to the site. The Doctor quickly discovered what was off about the reflection, which was that it was showing the reflection in the other way to a mirror and everything was in the right place. The Doctor also discovered scorch marks in a circular pattern surrounding the puddle, but left claiming he was no longer interested. As they left, the water started creeping away.

Bill later returned to St Luke's University only to see Heather there again, only drenched in water and repeating everything Bill was saying. Bill ran to the Doctor's office and shut the door behind her, locking it place with a chair. However the puddle managed to slide through the crack underneath the door and appear as Heather again. To test whether the 'alien menace' was after them or what was in his vault, he first takes his TARDIS to the vault where Nardole was. After he realises Heather was after them they run to the TARDIS and land in Sydney, Australia. The Heather Creature appeared there too.

The Doctor determined to find the limitations of the water, he travels to the future onto another planet. It's there he explains the the puddle was sentinent oil who found Heather as she wanted to leave, so it found a pilot whom it can leave through, though at the time his fascination with Bill was unknown. There a hand came out of a puddle of 'water' and attacked Bill. The Doctor saved her and went back into the TARDIS and lands in the middle of a Dalek-Movellan war to get the Dalek to exterminate the oil.

Upon doing so, the water survives the attack, saying the Dalek's "exterminate" phrase whilst doing so. When they see the oil, it has taken the form of a Dalek with Heather's star eye. It transforms again into Heather. The Doctor realises that the oil doesn't want to kill, but wants Bill. Bill tells him that Heather promised she wouldn't leave her which is why the oil keeps following her. The Doctor tells her to let her go, but the oil is determined and shows Bill how the oil sees Bill through their eyes, but is pulled back where the oil disappears. (TV: The Pilot)