The pressure comes as the Financial Services Authority (FSA) prepares to split into two new bodies: the Financial Conduct Authority and the Prudential Regulation Authority.
“It is absolutely vital the [new regulators] have people at the very top who understand the insurance industry they will be regulating,” said the Association of British Insurers.
Bronek Masojada, chief executive of Hiscox, said: “The naughty child is getting all the attention. The bankers got it so wrong that that is all anyone can think of at the moment.
“The view of the insurance sector is that if the organisation is run by a small number of people who are just central bankers and economists, then yet again it will be banking uber alles,” he added.
The FSA denied that insurers were being overlooked.