British Midland chairman Sir Michael Bishop said there would be "blood on the carpet" as budget airlines try to reposition themselves.
His comments came as British Midland revealed that profits for 1998 had tumbled by 34 per cent despite a record passenger total. Sir Michael said: "There will be some real blood on the carpet from the low-cost carriers at Stansted airport because people are coming into the market with a hybrid product that is neither one thing nor the other."
There were signs that budget airlines were moving away from the core concept, he said, highlighting Debonair's agreement to operate five aircraft on behalf of Lufthansa Cityline.
Sir Michael said British Midland had ruled out setting up a low-cost operation at Stansted, the London airport favoured by no-frills carriers.
He said budget airlines were not taking market share from British Midland. Its best routes in 1998 were Heathrow-Amsterdam, where it competes with easyJet, and Heathrow-Dublin, against Ryanair.
Pre-tax profits slipped from a record pounds 16.7m in 1997 to pounds 11.02m. Sir Michael said the fall was due to a pounds 5m "windfall" from the British Airways strike in 1997 and a pounds 4m start-up cost for a new London-Manchester service.
The Manchester service broke a 40-year BA monopoly. Sir Michael said the route moved into operating profit last month and his airline had taken a 30 per cent market share.
Turnover rose 3 per cent to pounds 558.8m and passenger numbers were up 5 per cent to six million.
British Midland has won licences to serve New York, Washington DC, Boston and Miami in the US, subject to a new bilateral air services agreement.