The financial watchdog has written to around 20 banks and other financial institutions asking about their connection to Panamanian law firm Mossack Fonseca.
The FCA gave firms a deadline of 15 April to undertake an initial review but there's still a "second tranche" of firms with a slightly later deadline.
McDermott said: It is far too early to give any view as to preliminary findings. The challenge is really working out what this 'iceberg' is: issues of quite serious criminality have been reported. There are things that may or may not be attractive but which may or may not be criminal.
McDermott stressed a significant amount of business in Panama would be expected to have been conducted legally.
At the beginning of April it was revealed in leaked documents from Mossack Fonseca that many of the world's most influential leaders had stashed money in tax-free offshore accounts, sparking international outrage and a raft of high-profile resignations.
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Tracey McDermott, who has been chief executive of the Financial Conduct Authority on an acting basis since September, made the comments during a hearing in front of the influential Treasury select committee.
John Griffith-Jones, the FCA chairman, gave evidence alongside her on topics ranging from the Panama Papers, to the watchdog's transparency, and the FCA's leadership changes.
McDermott was given the acting position after chancellor George Osborne stripped former FCA boss Martin Wheatley of the role following the Conservative's victory in the General Election last year.
Following the hearing Andrew Tyrie, chairman of the Treasury committee, said: Parliament’s, and the committee’s, role in the appointment and dismissal of the chief executive of the FCA has been greatly bolstered by the arrangements set out in this exchange of letters. As a result, parliament will now be better placed to safeguard the FCA’s independence, as John Griffiths-Jones, its chairman, clarified in evidence this morning. The scope for interference - or the perception of interference - by the Treasury or Treasury ministers is commensurately reduced.
Andrew Bailey, who heads its sister regulator the Prudential Regulation Authority, and is also the deputy governor of the Bank of England, will take over as head of the FCA in July. He was tipped last year as a possible successor to governor Mark Carney when he leaves the role.
Before his appointment McDermott announced she would take herself out of the running for the job. Four candidates were interviewed, with a short list of two drawn up before Bailey was put forward.
Griffith-Jones defended Bailey's appointment despite him not being interviewed for the role.
This was the HM Treasury process. The decision to ask Andrew [Bailey] was taken in good faith. It was the Treasury's decision and was in my opinion a perfectly reasonable one. I didn't know which way the chancellor [George Osborne] would go before he did, as it were.
Bailey’s replacement will be Sam Woods, the current head of insurance at the PRA.