The fund, which owns more than 5 percent of the exchange, said in a letter reviewed by Reuters that it wanted Rolet's contract to be extended to 2021 and asked the company to suspend the search for a new CEO immediately.

LSE announced last month that Rolet would be stepping down as its chief executive by the end of 2018.

TCI said it had met with Brydon and a senior independent director earlier this week and did not get a satisfactory answer for Rolet's departure. The fund called on Brydon to step down and start a search for a new chairman.

The fund also added that it would call for a Extraordinary General Meeting if Rolet was not retained as CEO.

LSE was not immediately available for comment, while TCI did not give any additional comment.

(Reporting by Maiya Keidan in London and Shubham Kalia in Bengaluru, editing by David Evans)