Bluebell said in a letter to GSK Chairman Jonathan Symonds that chief executive Emma Walmsley should reapply for her job as she would have "renewed credibility both internally and externally", the FT report said.

Earlier this year, activist Elliott had also taken a stake in GSK, calling for a leadership change at the company. Bluebell was largely backing Elliott's demands, the FT said.

GSK confirmed Bluebell had made demands in a letter.

"We continue to engage extensively with our shareholders with over 500 meetings so far this year," GSK said in a statement.

"They have expressed widespread and strong support for our plans to deliver a step-change in growth and performance, and given clear direction to focus on execution," the company added.

The British pharma major, with a market value of over 71 billion pounds ($96.95 billion), in July rejected Elliott's demands to change its board and sell its consumer healthcare arm.

GSK has set out plans to turn its consumer healthcare arm into a separately listed company, in a move that will deliver an 8 billion pound windfall and other financial benefits to boost drug development at its underperforming pharma business.

Bluebell was part of a successful investor campaign to oust Danone chairman and chief executive Emmanuel Faber in March.

($1 = 0.7323 pounds)

(Reporting by Aditi Sebastian in Bengaluru and Ludwig Burger in Frankfurt. Editing by Jane Merriman)