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)

Bernice Summerfield considered the task of writing an entire autobiography within ten days while being watched by two bounty hunters to be one that would vex Aladdin. (PROSE: The Dead Men Diaries)