Direct Line has stepped up to the challenge from a listed Esure by warning that there was "no room for complacency".
The company, which was spun out of Royal Bank of Scotland last year, admitted that the motor-insurance industry was likely to become even more competitive this year but said it expected to remain the market leader.
Direct Line shares have risen about 20 per cent since they were listed on the London Stock Exchange in October. Smaller rival Esure, which is run by Direct Line's founder Peter Wood, is set to follow suit over the next few weeks and has vowed to use the £50m it raises from the float to pay down debt and expand its market share.
Paul Geddes, Direct Line's chief executive, said his company was well-placed to build on its initial success: "There is no room for complacency as we face a competitive market, particularly in UK motor, where there are also expected to be significant legal reforms."