Cat Rock Capital, which holds just shy of 2% of Just Eat shares and has been pushing for a strategic shift at the company over the past few months, released a new open letter to directors on Monday.
The document said that while the US hedge fund continued to see “significant growth potential”, it accused the board of repeating past mistakes following the departure of chief executive Peter Plumb last month.
He had been appointed just 16 months earlier from moneysavingexpert.com and had presided over a period of investment in Just Eat’s systems at the expense of profits, Cat Rock claimed.
The hedge fund’s letter suggested the board was about to appoint another executive without specialism in running a food delivery business to succeed Mr Plumb.
Cat Rock, which had previously urged a sale of Just Eat, said it had failed to keep pace with rivals such as Deliveroo and Takeaway.com.
Its founder, Alex Captain, wrote: “Any new CEO will face the daunting task of rebuilding Just Eat’s entire management team while simultaneously attempting to execute on the company’s marketplace and delivery initiatives.
“We and our fellow shareholders believe this is not a task for a Plumb-style learner.
“Not surprisingly, the most accomplished industry leaders are already leading other online food delivery companies.
“It is therefore increasingly clear that a merger would be the best way for Just Eat to secure the management talent and delivery expertise it needs to compete.”
He continued: “We have spoken with many other shareholders, and many of them share our conclusion – a fair merger is a far better alternative than relying on the board, with its poor record of executive selection, to choose a new leader for the company.”
Just Eat shares – which lost ground last year but are 21% up in the year to date – rose by nearly 4%.
The company is due to report full-year results on 6 March having raised its guidance in January.
A spokesperson told Sky News on Monday: “We take communications with all our shareholders extremely seriously.
“As announced previously, we are carrying out a thorough CEO appointment process and we will update the market as appropriate.”