In a letter to Chairman Donald Brydon dated Nov. 7, Chris Hohn, founder of The Children's Investment Fund, reiterated his belief that Rolet was being forced out against his wishes, and repeated his threat to call a meeting to vote on removing Brydon if the company failed to act.
Hohn called on Brydon to waive a confidentiality agreement TCI said had been signed by Rolet covering the reasons behind his departure.
The LSE declined to comment.
TCI - the fourth-biggest investor in LSE with a more than 5 percent stake, Thomson Reuters data shows - first raised its concerns in a letter to the board last Friday, which prompted the LSE to say it had followed good governance.
"Confidentiality agreements which prohibit proper explanations to shareholders are bad corporate governance. Hence we refute your assertion that you followed proper governance procedures on succession planning," Hohn wrote.
"We ask you to waive immediately all confidentiality agreements on Xavier Rolet so that shareholders can now hear the truth and make informed judgements on the expected EGM [Extraordinary General Meeting] regarding your continued chairmanship and the retention of Xavier Rolet as CEO," it said.
(Reporting by Simon Jessop and Noor Zainab Hussain, editing by Louise Heavens)