Critics of the EU have said that leaving the bloc would mean Britain could determine its own financial rules and not be burdened with the bloc's regulation.
But Bailey told parliament's Treasury Select Committee that it would be "disastrous" to return to the light-touch bank capital regulation in place before the 2007-09 financial crisis, which left the public having to bail out lenders.
He threw cold water on claims that leaving the EU would mean a "bonfire of red tape", saying Britain would have to have rules that were as strict as the countries it traded with.
"You wouldn't immediately assume there is a sort of golden world out there where it's all different," Bailey said, noting the United States' extensive regulatory framework.
Tracey McDermott, acting chief executive of the Financial Conduct Authority, told the committee, that being outside the EU would allow her to make slight changes, but that bank conduct regulation would remain much the same.
(Reporting by Huw Jones, editing by David Milliken)
