Lord Turner warns that the process of businesses, households, banks and the government trying to cut their big debts built up in the boom years, what is known as deleveraging, may bear down on the British economy's ability to grow for many years yet.
He is also concerned that quantitative easing, or the purchase by the Bank of England of government debt, may be becoming less and less effective in promoting a recovery.
So the City's top regulator, who is seen as one of the two leading candidates to be the next governor of the Bank of England, says that the government and the Bank may have to consider new unorthodox policies to overcome what he calls the powerful economic headwinds.
Although he does not make explicit what he means by these innovations, it is understood he believes the Bank of England should consider telling the Treasury it never has to repay some of the £375bn of government debts the Bank acquired through quantitative easing - which many conventional economists would regard with horror, because it would be seen as the government, in effect, printing money to finance public spending.
Since some of this debt is due for repayment next year, the Bank of England has a deadline for deciding whether to roll it over into a perpetual zero-interest debt - which would be seen as, in effect, writing off the debt.
The economists' slang for this kind of policy is the creation of "helicopter" money, because it is seen as the equivalent of dropping money on all of us from out of a helicopter (see this column by Simon Jenkins for more on this).
Lord Turner, in what will be his last speech to the City at the Mansion House in his current role, also broke something of a taboo among prominent British ministers and officials by speaking openly about how if the eurozone cannot save itself through making bold reforms, it should attempt to dissolve itself in what he called a "controlled rather than chaotic fashion".