Ryanair's Michael O'Leary said BMI's low-cost offshoot, BmiBaby, and Exeter-based airline FlyBEBudget airlines were doomed to fail given the prolonged "bloodbath" in the budget travel industry.
He also said two German budget airlines, Germanwings and Hapag Lloyd Express, might not stay aloft either. All four carriers are suffering heavy, sustained losses, he said.
"We believe some of these loss-makers will go bust, some over this winter, some over the next two years," he said. "They're not all going to survive. They can't all sustain this level of losses for too long."
Low-cost carriers in Europe are struggling to find profitable territories, conventional hub-and-spoke airlines have lowered fares aggressively, and the high price of oil has compounded the financial squeeze.
Ryanair, Europe's largest low-cost airline, also said that in this year's first quarter it posted its first losses ever.
Notable deaths of 2014 [PHOTOS]