Ike Ekweremadu, 60, and Beatrice Nwanneka Ekweremadu, 55, are alleged to have transported a 21-year-old man from Nigeria to London.
Prosecutors allege the couple planned to have his kidney removed so it could be given to their daughter.
The Ekweremadus will next appear at the Old Bailey on 4 August.
The alleged victim is said to have refused to consent to the procedure after undergoing tests at the Royal Free Hospital in Hampstead.
It is alleged the Ekweremadus treated him as a slave before he escaped and went to Staines police station, Surrey.
The couple were arrested at Heathrow Airport on 21 June after arriving on a flight from Turkey.
Remanded in custody
They both appeared in the dock at Westminster Magistrates’ Court earlier on Thursday following previous hearings at Uxbridge Magistrates’ Court last month.
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Mr Ekweremadu is charged with conspiracy to arrange or facilitate travel of another person with a view to exploitation, while his wife is charged with arranging or facilitating travel of another person with a view to exploitation.
The couple were not asked to enter pleas, but the court heard they have indicated not guilty pleas.
They deny there was a criminal conspiracy, and will say no exploitation occurred, it was said.
Deputy chief magistrate Tan Ikram remanded them in custody ahead of their next appearance at the Old Bailey.
He lifted a reporting restriction on the complainant, who was previously described as a child.
Due to the nature of the charge, the complainant still has anonymity despite the fact he is over 18.
The Ekweremadus will appear at the Central Criminal Court in London on August 4 for the continuation of the trial. As reported earlier, the alleged victim, David Ukpo, is no longer considered a minor after it was revealed that he is indeed 21 years old.
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-BBC.com