Police in Essex had concluded no further action was needed over one allegation in the Channel 4 investigation, while the Church of England said its investigation had also found no case to answer.
However, church leaders called for Bishop Perumbalath to step aside, saying his position was “untenable”.
Julie Conalty, the Bishop of Birkenhead and deputy lead bishop for safeguarding, agreed that Bishop Perumbalath “needed to step back” but said he had not had “the chance to defend himself”.
The bishop told Radio 4: “It feels to me that it may have been unfair to all parties.
“It strikes me that the bishop has not had a chance to defend himself in tribunal and nor have the complainants been able to go to tribunal with the complaint.”
She said there were questions over whether church processes served both victims and those who had been accused.
“Our complaint processes are not trauma-informed, they don’t serve victims and survivors well,” she added.
She added that the church needed to have a “more open conversation” about misogyny faced by female clergy.
The Church of England has been contacted for comment.