Ike Ekweremadu, 60, is accused with his wife, Beatrice, 56, their daughter, Sonia, 25, and a doctor of bringing a 21-year-old man from Nigeria to have his kidney removed.
The man is said to have raised the alarm after refusing to consent to the procedure, following preliminary tests at a north London hospital.
Charges were brought after the man walked into a police station and the Ekweremadus were arrested at London's Heathrow airport in June.
The Ekweremadus and the doctor, Obina Obeta, 50, are accused of conspiracy to arrange the travel of another person with a view to exploitation.
The alleged offence is alleged to have taken place between August 1 last year and May 5 this year.
No pleas were entered when they appeared at London's Central Criminal Court, also known as the Old Bailey, on Monday.
The kidney was intended to be used for Sonia, prosecutors claim.
Judge Mark Lucraft set another hearing date for December 16 and brought forward the defendants' trial from May to January 31.
Ekweremadu and Obeta were remanded in custody.
Beatrice and Sonia Ekweremadu were released on conditional bail