Aladdin

Aladdin was the title character in the popular fairy tale "Aladdin and His Wonderful Lamp", often adapted into pantomime. Jo Grant played Aladdin in a UNIT staff Christmas panto in the 1970s, with Mike Yates as Widow Twankey and the Third Doctor as the wicked sorcerer. (PROSE: Timewyrm: Revelation, No Future)

Minor references
Jo likened Omega's palace to Aladdin's magic cave, while the Second Doctor made a similar analogy of the singularity to Aladdin's magic lamp. (TV: The Three Doctors)

Charley Pollard compared Ike's shop to Aladdin's cave. (AUDIO: Sword of Orion)

Iris Wildthyme compared Bianca's dressing room to Aladdin's cave. (AUDIO: The Wormery)

Pickens compared Thomas Brewster's private room to Aladdin's cave. (AUDIO: The Haunting of Thomas Brewster)

Sarah Jane Smith reportedly called the Cyberman invasion (TV: The Tenth Planet) "The Aladdin's lamp of applied technology," since humans were able to salvage technology from the abandoned Cyberships and advance research into space travel. (PROSE: The Power of the Daleks)

Sabalom Glitz asked the Sixth Doctor if he, as a Time Lord, had a magic lamp to rub. (TV: The Mysterious Planet)