In an interview with BBC News 24's Business Today programme Sir Howard said he was concerned at the high borrowing levels in some parts of the country.
And he said he would not be surprised if there was downturn in house prices in London and the South East of England.
Earlier this month, house price data from the Halifax bank showed house prices rising by 4.2% during May - the fastest rate since records began in 1983.
The news has raised fears that the housing market is getting out of control, and that house prices could be heading for a crash similar to the one seen in the early 1990s.
Last week the Bank of England's deputy governor David Clementi warned that the current rate of increase in house prices was not sustainable.
And he warned that if high levels of borrowing continued, the price adjustment could be "quite severe".
Heading for a fall?
Sir Howard told the Business Today programme that he was particularly concerned that in London and the South East of England, some people were taking out mortgages on very high multiples of income, and often with little or no deposit.
"In those cases we believe there are some risky loans out there," he said.
"Some people are taking on obligations which they may well live to regret, particularly if we do see a downturn in house prices in London and the South East, which would not be surprising.
"We believe that, selectively, there is some concern about the mortgage market but it is not concern everywhere.
"It is concern about over-borrowed, young professionals in areas where house prices have risen very sharply indeed."
Financial strength
Sir Howard also said the recent falls on the stock market had led the FSA to monitor the life assurance sector.
Concern has risen recently that the financial strength of some firms has weakened.
"We are monitoring the whole sector very closely but there are obviously some (companies) that are financially stronger than others," he said.
When asked how loudly the alarm bells are ringing he said: "I can hear them."
Sir Howard also criticised the complexity of "with-profits" savings funds - which are used by many people to save for mortgage repayments and pensions.
"At the moment, 'with-profits' for many people is a sort of black box, they do not understand what it is they have got."
"The whole terminology is unsatisfactory and really ought to be changed, and the industry has not helped itself by dressing up these products in obscure language."