He is accused of bringing a 21-year-old man from Nigeria to have his kidney removed, along with his wife Beatrice, daughter Sonia and a doctor.
According to the prosecutor, the defendants allegedly planned to remove a kidney from the man so that it could be given to Sonia.
He was unable to attend court because he is in the hospital with an unspecified condition.
His defense team has also submitted a psychological report, saying he is unfit to stand trial.
The court adjourned the meeting shortly after so prosecutors could read the report.
The accuser reportedly raised the alarm after refusing to consent to the procedure following preliminary tests at a north London hospital.
Charges were filed after the man went to the police. The Ekweremadus were arrested in June last year at London’s Heathrow Airport after flying to the UK.
Another man, Obinna Obeta, a 50-year-old doctor from south London, was later arrested.
The trial has been postponed from the scheduled date in May.
Ekweremadu is a senator from the opposition Peoples Democratic Party in Enugu state in southeastern Nigeria.
Ekweremadus and the doctor are charged with conspiracy to arrange the travel of another person for the purpose of exploitation, under UK modern slavery legislation.
The breach is believed to have taken place between August 2021 and May 2022.
Ike Ekweremadu had his bail application rejected over concerns that he might flee Britain.
Obeta was also arrested. Beatrice and Sonia Ekweremadu are on conditional bail.
Beatrice, dressed in all black, sat next to her husband in the dock during the brief session on Tuesday morning.
Supporters and protesters gathered around the London court ahead of Tuesday’s hearing.
“I mean, this case is unbelievable,” said protester Citizen Gbola.
“Where else in the world would you have a vice president of the Senate, who is still a senator, getting his regular salary?”