Just Eat should merge with a rival online meal delivery company because the board has shown that it can't find a suitable chief executive, according to Cat Rock Capital Management, which owns about 2 per cent of the company.

The Greenwich, Connecticut-based investment firm sent an open letter to Just Eat's board of directors saying it had made a mistake in appointing Peter Plumb as chief executive in 2017. Just Eat should use global consolidation to its advantage and a merger would deliver "real value," according to Cat Rock.

A spokesman for Just Eat said it takes communications with all of its shareholders “extremely seriously”, adding that it is “carrying out a thorough CEO appointment process and we will update the market as appropriate”.

Mr Plumb stepped down last month, and Cat Rock said Just Eat has ignored two suggestions of potential replacements, who have experience in online food delivery. The stock has dropped 12 per cent in the past 12 months and several key executives resigned during Mr Plumb's tenure, including former chief operating officer Adrian Blair. – Bloomberg