Nigerian-trained doctors are among the largest groups of international medical professionals serving the NHS.
The president is expected to return to Nigeria at the conclusion of the state visit.
They were released on conditional bail on Wednesday night until December 12 while enquiries continue, according to the force.
It has been widely reported that the king was keen to resume some form of public duties in spite of his illness.
British King Charles III will address the French Senate on Thursday for the first time.
Mr Harry, 38, was smiling as he arrived at the abbey dressed in a morning suit and with medals on his chest.
