An alien spaceship crashed in Oxford in 985. Matilda and her two sisters saw it and went to see more. They found the three pilots dying, who asked them to take over for them. If they did not, the damaged ship would explode and destroy the Earth. The sisters consented and were never seen by the outside world again.
The ship extended their lives, but by 1481 the power drain meant that one of them would die soon. They sent astral projections of themselves to the nearby convent and lured one of the nuns to the ship as a replacement. Only young women were susceptible to the hypnotic influence. Unfortunately, another was needed in half the time (1729) and half again (1853). This continued until by 1977 a new girl was required every few months. The Fourth Doctor and Leela were able to discover the truth hidden by the College for centuries, rescue the girls and repair the ship enough so the explosion did not blow up the planet. (AUDIO: The Cloisters of Terror)