Highway Insurance said it does not intend to replace departed chief executive Andrew Gibson.
Gibson was poached by Neil Utley to take up the role of finance and operations director at Cox.
Chris Hill, the new managing director of Highway Insurance Company, the company's FSA-regulated entity, said: "We made a collective decision that the most important thing was management continuity.
"Andrew put us on a very strong footing and we wish him every success, but we feel there is no real need to find a replacement."
Paul Cosh remains managing director of the group's retail arm, while Ian Patrick remains group finance and operations director.
Hill said: "Our strategy is largely unchanged. In difficult market conditions it is about discipline and strong underwriting.
"We have proved we are capable of that, posting a 30% return on equity last year despite falling rates."
He added"We will make sure the business we write is profitable and wait for conditions to improve."
