Madge Arwell was the mother of Cyril and Lily Arwell and was briefly a companion of the Eleventh Doctor. She was a terrible driver, with a tendency to bump into things even when parked. Her husband, Reg Arwell, was a bomber pilot in the Second World War.
Madge had helped out the Doctor in 1938 when he fell from a sub-orbital spaceship into a field she was cycling past. He told her he would return the favour if she made a wish. The Doctor kept his word and returned in 1941 to give her children the "best Christmas ever", following her receiving a telegram indicating that Reg was missing and presumed dead.
Her piloting of the ship built by the Adrozani Forest's King and Queen saved her children, the Androzani Forest's life force, and provided the lost Reg with a light to follow home, which he did, through the Time Vortex, landing safely on Christmas Day, with his family.
Later, as the Doctor bade farewell to her, Madge insisted he spend Christmas day with family. Madge's persistence led to the Doctor visiting his in-laws, Amy Pond and Rory Williams, for Christmas dinner in 2013. (TV: The Doctor, the Widow and the Wardrobe)
Madge had a habit of taking in "waifs and strays" and could even come across as slightly dotty. When her family was threatened, she revealed a steely determination, pulling a gun on the harvest rangers, taking control of their futuristic tripod, braving acid rain and piloting through the time-space vortex with a forest in her head. She was also kind enough to help strangers in need. (TV: The Doctor, the Widow and the Wardrobe)