Their daughter Sonia needs a kidney transplant, but their efforts to find a donor failed.
The pair is being accused of organ harvesting, a crime punishable by 10 years in prison. The claimed crime entails the removal of body parts against the victim's will.
The detectives of the Metropolitan Police's Specialist Crime Team picked them up from the airport and took them away for questioning.
Yesterday, they were brought to the Uxbridge Magistrate's Court close to the airport.
Yesterday, the court hosted a delegation from the High Commission led by the head of the section responsible for consular and welfare services.
The ex-Deputy Senate President and his wife have used consular assistance.
According to a diplomatic source, if proven guilty of the couple's crimes, they might face a 10-year prison sentence.
"In the UK, 10 years in prison is the maximum punishment for certain crimes that have been proven.
It is also possible to seize their assets in the UK.
The judge denied them bail and fixed July 7 for a ruling on jurisdiction.
In other news, the Labour Party Presidential candidate, Mr. Peter Obi, reacted to his ex-deputy and wife's detention over human trafficking charges levelled against them in the UK.
Taking to the micro-blogging platform, Twitter, Peter Obi offered prayers to their daughter who is in a delicate health condition.
"My family and I are with the Ekweremadu’s over their travail. We join all men of goodwill in praying for the healing of their daughter and commit them into God’s hand for justice to be done. -PO" he wrote.