AVIVA PLC 
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The move follows complaints from the insurance industry body, which called on the Financial Conduct Authority (FCA) to learn lessons from the incident, but stopped short of demanding the removal of senior staff.
When some of the review's details were published in a newspaper last month, shares in insurers including Aviva, Prudential and Legal & General fell sharply. Insurance bosses were angered as they waited several hours for the regulator to outline its full intentions.
The incident was described by Martin Wheatley, head of the FCA, as "not our finest hour".
On Tuesday, the regulator said it had appointed Simon Davis, a partner at law firm Clifford Chance, to conduct an inquiry into the affair, which it added would be overseen by a committee of non-executive FCA board members.
The FCA set out "terms of reference" for the inquiry which followed closely what British finance minister George Osborne laid out in a letter to the regulator last week.
It was not immediately clear, however, whether the inquiry would satisfy the regulator's critics.
In a letter to the FCA sent on April 1 and released to the media on Tuesday, the Association of British Insurers (ABI) said the regulator "cannot be permitted to investigate itself".
It declined to comment when asked if it was satisfied with the framework of the inquiry announced by the FCA on Tuesday.
"This is very much a situation in which even the perception of a lack of objectivity or thoroughness could be damaging to the FCA and its aims," ABI Director General Otto Thoresen said in the letter.
Thoresen told a committee of lawmakers on Tuesday that he was not seeking Wheatley's removal over the incident but stressed "the importance of learning lessons" and was critical of the FCA's slowness in clarifying its position.
"We didn't have a press release, we didn't have a report against which we could compare what was being said," he told the Treasury Select Committee. "And until we did ... it was very, very difficult to give people confidence."
The committee's chairman, Andrew Tyrie, said it would shortly be meeting the lawyer leading the FCA inquiry.
"It is vital that this investigation is wholly independent of the regulator," Tyrie said in a statement.
Asked whether investors would have grounds for taking legal action against the FCA over the incident, Thoresen said that was "a definite question" but it would have to await the outcome of the internal review of the FCA.
(Editing by Chris Vellacott and Mark Potter)
By Jemima Kelly and Huw Jones
