Cat Rock Capital, which owns 2% of the firm, on Monday urged the food delivery firm in an open letter to merge with a “well-run industry peer”.
This, it said, was a better outcome than “relying on the board to choose a new CEO” following the departure of boss Peter Plumb last month.
Cat Rock’s letter read: “Since Mr Plumb’s departure, we have attempted to work with the board constructively and privately to achieve the best possible outcome for all Just Eat shareholders.
“Unfortunately, recent developments have made it clear that the board is squarely on the path to repeat the serious mistakes that led to Mr Plumb’s appointment.
“Cat Rock argues that a merger with a well-run industry peer would be a far better outcome for shareholders than relying on the board to choose a new CEO.”
A merger would deliver “world class management, delivery capabilities, a premium” and value creation, the group added.
The investor went on to complain about the departure of Chris Simair, chief executive of Just Eat’s Canadian business SkipThe Dishes, who has been replaced by marketing man Kevin Edwards.
“Ignoring the Plumb lesson, Just Eat shockingly entrusted the leadership of this crucial business to the former chief marketing officer of the Movember Foundation, a not-for-profit organisation that gets men to grow moustaches.”
Chief customer officer Peter Duffy is acting as interim chief executive of the group while Mr Plumb’s replacement is found.
This is the second time Cat Rock has sunk its claws into Just Eat.
It recently described the firm as the worst-performing online food firm in the world as it called for a radical shake-up.
The US investment firm also wants Just Eat to sell off non-core assets, such as its interest in the iFood business in Brazil and other non-European businesses.
Just Eat is desperately attempting to keep up with Deliveroo and Uber, firms that have been muscling in on its territory of late.
Speculation that Uber is in early talks to buy rival Deliveroo has also recently hit Just Eat’s shares.